In 1590 Abraham Ortelius published a new supplement, Additamentum IV, to his collection of maps, Theatrum orbis terrarum. Amongst the new maps is a map of Iceland (Islandia). The author is not mentioned but on it says that it was engraved in the year 1585. On it we can also find a dedication to Frederick II of Denmark by Andreas Velleius (Andreas Sørensen Vedel); a well-known Danish historian of the period. It has been known for a long time that Vedel is not the author of the map and he could not have made it. The map is so superior to all earlier maps of Iceland in content and execution that an Icelander must be its originator. All clues point in the direction of Gudbrandur Thorláksson, bishop of Hólar. In his school days in Copenhagen he had studied mathematics and astronomy alongside theology. He had calculated the position of Hólar and arrived at an amazingly accurate result. He made a map of the North in 1606. The map of Iceland by bishop Gudbrandur does no longer exist and it is not known when he made it or what resources he had at his disposal. A list of churches and fiords has been found which he seems to have used, especially the latter, which he follows very closely for a large part of the coast.Ortelius seems to have received the map directly from Vedel's own hands, and probably it never occurred to him that Vedel was not the author. At about this time, Vedel was writing a history of Denmark, which in fact never appeared, which was to be accompanied by maps. Nothing is known of any contact between Vedel and the bishop, but it is not unreasonable to suppose that Vedel should have turned directly to the bishop for assistance in this respect, it was customary at this time to supplement historical writings with geographical introduction and explanatory maps. Some of the information that Ortelius gives about Iceland on the back of his map is taken directly from Vedel.
Ortelius' map of Iceland was for a long time attributed to Vedel, although even in the time of bishop Gudbrandur it was known that he was not the author. A contemporary of the bishop, the Danish historian Lyschander, attributes the map to the bishop without further comment, and the same applies to bishop Finnur Jónsson in his Ecclesiastical History.
On his map Ortelius does not follow the calculations that bishop Gudbrandur had made on the latitude and longitude of the see at Hólar. It is not known when Gudbrandur completed his calculations, it may be after he handed over the map.
The ocean is provided with a large number of whales and monsters, which can hardly have accompanied the original. They, along with polar bears, driftwood and sea ice, are marked with the letters A-Q which refer to explanations on the back of the map. Some of the information regarding these creatures may have come originally from Iceland, perhaps from bishop Gudbrandur by way of Vedel, who is given as authority for some of it. This would then have been added to and mixed with foreign fables and inflations. Most of the pictures can be traced originally to Olaus Magnus, though the immediate source is more probably Sebastian Münster, who adopted many of the former's drawings in his Kosmographia (1544); with minor changes. It is not out of the question that some such drawings may have accompanied bishop Gudbrandur's map, since he was a most accomplished draughtsman. In the text on the map itself there are various accounts which can probably be traced chiefly to Icelandic tales and superstitions, whether or not they were to be found on the bishop's own map.
The map has roughly 250 names, many of them rather distorted, though not so much as to be unrecognisable. In many cases they are given a Danish form, but there is no way of knowing whether this is the work of the Danish intermediary or whether the bishop himself made the changes for the convenience of his Danish readers. Some forms clearly represent misreadings of the bishop's handwriting, arising from his use of insular letter forms, which was long in the custom in Iceland though quite unknown elsewhere at this time.
Although the map is faulty in many ways, it is far superior to all earlier maps of Iceland in content and execution. Here for the first time we find a map giving a more or less complete survey of all settlements in the country and most places of interest. Apart from this the most striking thing is how angular the country is, with very prominent headlands. The south and east coasts are far too straight instead of being curved. The width is too great in relation to the length, a tendency which continued to plague maps of Iceland for a long time. The country is also placed too far north. The central highlands are extremely poorly represented, amazingly little being known about them then and indeed much later. Most of the principal glaciers, however, are marked on the map, though Vatnajökull, the largest glacier in Europe is missing.
Bishop Gudbrandur's map of Iceland in the version by Abraham Ortelius was printed without change from the same plates in every subsequent edition of the book in various languages after 1590, until publishing was discontinued in 1612. In Latin 1591, 1592, [1595], 1601, 1603, 1608 and 1612; French 1598; Dutch 1598; German 1602; Spanish 1606 and 1612; English 1606; and Italian 1608 and 1612. It is often difficult to see from what edition of the collection a particular map is. Most copies of the map that exist have been taken from editions of the book which have been torn up and the maps sold as individual sheets. Many copies have been coloured. It is estimated that around 4,150 copies of the map were printed.
The term of the old maps as represented in Carta marina by Olaus Magnus was now over, and most cartographers took bishop Gudbrandur's map as their starting point. Ortelius was first on the spot, forcing others to follow him.

On the back of map is a description of Iceland and various explanations of what appears on the front. Here is this text from the English edition of the map:

I S L A N D

I Do find in the Ecclesiasticall history lately set forth and imprinted vnder the name of M. Adams: That the people of this Iland came vnto Adelbert Bishop of Breme, earnestly entreating him to appoint them some learned diuines that might be able to preach the Gospell and plant Christianity amongst them. Neither do I thinke that there is any mention of this Nation in any other more ancient writer than he. Although I must confesse, that Sigebertus Gemblacensis hath left record, that Great King Arthur, about the yeare of Christ 470. subdued this island and reduced the people to his obedience. This I take as a fable, not for any true history. For I do certainly know that this was neuer written by Sigebert, but shuttled in, as many things els, by some other. For a very faire Manuscript copy of mine owne, as also another in parchment of my friend, haue it not.) Now this Adelbert died about the yeare after Christs incarnation 1070. And that the name Thule, oft spoken of almost by all old writers aswell Poets and Historians as Geographers, doth not pertaine to this Iland (against the opinion well neere of all the learned men of our time) but rather to Scone (Scandia Peninsula) a neck-land of Norway, not only the authority of Procopius; a graue discreet writer; but also for that a note and remnant of that name yet remaineth to this day in Scone, in that part which is opposite to the Orkeney iles; namely in a place of Norway where the famous Mart of the Belgæ is seated. For amongst other shires of Norway there is one in this place which they call Tilemarcke, that is, the March or shire of Tule. The islands also oueragainst this shore which vulgarly are called Hetland and Shetland, and the seamen, as I vnderstand out of England by the relation of my good friend M. W. Camden, are commonly called Thylinsel, whereby I conceiue that this Iland tooke the name from the next maine land opposite vnto it. For what els is Thilinsel, but the iland of Thile? This opinion of mine not only Pomponius Mela doth confirme, who writeth that Thule was opposite to the sea coast of the Belgæ; (he directly saith, I say Belgarum, not Britannorum litteri, the sea coast of Britaine where indeed Island is situate, not Thule:) but also Ptolemy the prince of all Geographers and writers in that argument, who placeth Thule vnder the 29. degree of Longitude, and 63. of Latitude. Which position and calculation of degrees doth exactly and precisely fall vpon Tilemarcke. And as for Island there is no man that hath looked with halfe an eie into Geographicall Mappes and Charts, but doth know it to lie vnder the first degree of Longitude, and the sixtieth degree of Latitude. And I perswade my selfe euen Arngrimus Ionas himselfe, an Islander borne, in that his Treatise of Island, where he saith that the latitude of this Iland is about 44. degrees and 45. minutes was much deceiued. It is therefore as cleare as the noone day, as he saith, that Island is not the same that Thule was: and the same Procopius saith, that it is inhabited by thirteen Nations, and gouerned by so many Kings, and to be tenne times as great as Brittaine: so that not without good cause Stephanus giueth it the title of Great; when as it is certaine that Island is much lesse than Brittaine. The same Procopius affirmeth that the Scritifinni, a kind of people so called, did inhabite Thule; these Diaconus nameth Strictofinni: and speaketh of them in Scandia; as doth also Iornandes in his history; notwithstanding he corruptly calleth them (that I may note this by the way) Crefennæ. Thus, gentle Reader, thou seeth that which they name Scandia or Scone, he calleth Thule: and the same nation to this day dwelleth in the same Scandia, called by the same name no whit corrupted. For they are called vulgarly Scrickefinner, and do dwell in Scandia, and not in Island. In Thule Procopius writeth, that there be huge great woods: in Island all the world knoweth there are none at all. And so Isacius vpon Lycophron saith truly, when he affirmeth that Thule, is vpon the East of Brittaine, not vpon the North, as is Island. Contrary to that which Strabo (a most worthy and diligent Geographer, by the sound iudgement of all the learned) saith of it, but from the relation, as there he addeth of Pytheas, a shamefull lying historiographer, whose custome was, as Diodorus Siculus in his second booke writeth, to counterfait and coine fables so cunningly that ordinarily they passed for true stories. This is that Thule, which Tacitus reporteth, when the Romane nauy sailed round about Brittaine was seen and viewed by them, but not regarded, and therefore not entered as is probable. This could not be Island, which is much farther off, and out of kenning. But this is enough in this place of Thule or Scandia. We will addresse our selues to speake of Island, an iland altogether vnknowen, and not once named in any ancient writer.
ISLAND, or, the Frosen or Icieland, which is all one, was so named of the ice which lieth continually vpon his North side: for there now beginneth the Frosen-sea, as Crantzius writeth. It was called SNELAND, of the Snow which all the yeare long doth heere in some places continue: Item GARDARSHOLM, that is, Garders ile, so called, as Arngrimus himselfe being an Islander borne writeth, of one Gardar a man so named who first found it or inhabited the same. This iland is an hundred Germane miles in length, as commonly most writers do hold; but the foresaid Arngrimus Ionas saith it is 144. miles long. For the most part it is not inhabited, but is wast and mountainous, especially toward the North part: by reason of the bitter blasts of the South winds, which will not suffer, as Olaus teacheth, so much as any low shrubbe or bush once to put forth his head. It is subject to the king of Norway, and so hath continued euer since the yeare of Christ 1260. at what time first, the same Arngrime affirmeth, they did their homage to that Crowne. Whereupon the king of Denmarke euery yeare sendeth thither a Lieutenant, by whom they are now gouerned, as in times past they were by certaine Bishops of their owne; by whom they were, as we said before, conuerted vnto Christianity, in the time of Adelbert Bishop of Breme. In the raigne of Harald with the faire lockes, (Pulchricomus, Harfagro they vulgarly called him as Ionas writeth) who was the first Monarch of Norway, it was first begun to be inhabited, as some would faine perswade: namely when he had ouercome the pety kings and had banished them out of Norway, they being driuen to seeke their dwelling in some other place, they forsooke their owne natiue country, shipped themselues together with their wiues, children, and whole families, landed at the length in this iland, and heere seated themselues. This seemeth to me to haue happened about the yeare of Christs incarnation 1000, but the forenamed authour Arngrinus Ionas saith that it was in the yeare 874. who also there setteth downe a Catalogue and names of all their Bishops. The first Bishop, as Crantzius writeth, was Isleff. That it was subiect to the command of the same Norweies about 200. yeares, I find in the abridgement of Zenies Eclogs, where I find that Zichmi king of Friesland attempted warre against this iland, but in vaine, and was repelled by a garrison of souldiers placed there by the king of Norway, to defend the same from the assault of enemies. It is diuided into foure parts or prouinces according to the foure quarters of the World: namely, into Westfiordung, Austlendingafiordung, Nordlingafiordung and Sundlendingafiordung, as to say as the West quarter, East quarter, North quarter and South quarter. It hath but two Bishops seas, Schalholdt, and Hola; with certaine scholes adioined vnto them. In the diocesse of Hola are Monasteries Pingore, Remested, Modur, and Munketuere. In the diocesse of Schalholdt are Videy, Pyrnebar, Kirkebar and Skirda. Yet by the letters of Velleius, the authour of this chart, which he wrote vnto me, I do vnderstand that there are heere nine monasteries: and besides them 329. churches. They haue no coine of their owne, nor cities: for the mountaines are to them in steed of cities, and fountaines for pleasure and delights, as Crantzius testifieth, who affirmeth that for the most part they dwell in caues, making their lodgings and roomes by cutting and digging them out in the sides of hilles. The which also Olaus doth testifie, especially in the winter time. They build their houses of fish bones, for want of wood. Contrariwise Ionas he saith, that heere are many churches and houses built reasonably faire and sumptuously of wood, stone and turffe. Wares they exchange with Merchants for other wares. Forrein dainties and pleasures they are not acquainted withall. They speake the Cimbrian language, or the ancient Germane tongue, into which we saw this other day the holy Scriptures translated, and imprinted at Hola (a place in the North part of this island) in a most goodly and faire letter, in the yeare of our Lord 1584. I say, in the old Germane tongue: for I do obserue it to be the same with that, in which a little booke that is imprinted vnder the name of Otfrides Gospels, is written in. Ionas himselfe confesseth that they haue no maner of cattell beside Horses, and Kine. Velleius witnesseth that they haue no trees but Berch and Iuniper. The soile is fatte for pastorage and the grasse so ranke, that all men that haue written of this iland do iontly and with one consent affirme, that except they do sometime fetch their cattell from the pasture and moderate their feeding, they wilbe in danger of being stopped vp with their owne fatte. Yet all in vaine oft times, as the same Arngrime affirmeth. The soile is not good for corne or for eareable ground, and so it beareth not any maner of graine, therefore for the most part they liue altogether on fish. Which also being dried and beaten, and as it were ground to meale they make into loaues and cakes, and do vse it at their tables in stead of bread. Their drinke in former time was faire water, but now of corne, brought vnto them from forren places, they haue learned to brew a kind of beere: so that after they began to trade with strangers resorting to them, they began also to loue better liquours and haue left their drinking of water. For as Georgius Bruno maketh me beleeue, the Lubekes, Hamburgers and Bremers do yearely resort to this iland, which thither do cary Meale, Bread, Beere, Wine, Aquavitæ, course English clothes and other such of low prices, both Wollen and Linnen, Iron, Steele, Tinne, Copper, Siluer, Mony both Siluer and Gold, Kniues, Shoes, Coifes and Kercheifes for women, and Wood whereof they build their houses and make their boats. For these they exchange the Island cloth, (they commonly call it Watman) huge lumps of Brimstone, and great store of dried fish, Stockefish we call it. All this out of the West and South parts of the same. Out of the East and North part of the iland, where there is great plenty of grasse, they transport into other countries, Mutton and Beefe, butter and sometime the fleece of sheep, and skinnes and pelts of other beasts, foxes and white falcons, horses, for the most part such as amble by nature without the reaching and breaking of any horse courser. Their oxen and kiue are all heere polled and without hornes: their sheepe are not so. Saxo Grammaticus and Olaus Magnus do tell of many wonders and strange works of God in this iland, whereof some it will not be amisse to receit in this place. But especially the mount Hekla, which continually burneth like vnto Ætna in Sicilia, although alwaies those flames do not appeare, but at certaine times, as Arngrimus Ionas writeth, and affirmeth to be recorded in their histories, as namely in the yeare 1104, 1157, 1222, 1300, 1341, 1362, 1389, and 1558, which was the last time that the fire brake out of this hill. Of the like nature is another hill, which they call Helgafell, that is, the Holy mount. Of the which mountaine the forenamed Bruno, a laborious student, and for that his worthy worke which he hath set out of all the cities of the World, famous and knowen farre and neere all the World ouer, hath written in his priuate letters vnto me, that in the yeare 1580. (Ionas saith it fell out in the yeare 1581.) not in Hecla, but in another mount, namely, in Helgefel, fire and stones were cast out with such crackes, thundering and hideous noise, that fourescore miles off one would haue thought great ordenance and double canons had been discharged heere. At this hill there is an huge gulfe, where spirits of men lately departed, do offer themselues so plainely to be seene and discerned of those that sometime knew them in their life time, that they are often taken for liuing men of such as are not aware that they are dead: neither do they perceiue that they were deceiued, untill the Ghosts be gone. (Ionas accounteth this for a fable.) There are also certaine spirits or ghosts, which do shew themselues apparantly to be seen in the businesses of mortall men, or of such as came to their end by some violent mischance, as Olaus reporteth. They call these Drols, as Ruhmayer testifieth. (Now Drol, is a giant of the mountaines, if we may beleeue Arngrime Ionas an Islander by birth and bringing vp) Heere is a spring which by reason of a filthy smoaking water which runneth from it, killeth any thing that naturally the earth bringeth forth: and whatsoeuer is besmered with this smokie fume, in continuance of time becommeth as hard as a stone, yet still retaining the shape that it had before. There is also a spring of pestilent waters, which whosoeuer shall tast or drinke of, will presently be as if he had drunke poison. Heere also are certaine waters that are in propertie and tast somewhat like drinke that is made of mault. There are fires heere, that will not burne or consume flax, yet they will quire drie vp and consume water. They haue beares, crowes, and white hares. As also Eagles with white tailes, as our authour Ionas the Islander whom we haue often cited, doth witnesse. These Pliny (as he there alleageth) Pygargos, I thinke we call them Wringtailes. But those that are desirous to know all the strange wonders of this iland let them read Albert Crantz, Saxo Grammaticus, Iohannes Magnus, and Olaus Magnus, whom they may beleeue or not beleeue, according as they shall find cause: To those they may adioine that which David Chytræus in his Saxon history hath written of this iland. Except I be deceiued, the fable which Isacius vpon Lycophron reciteth, of a certaine iland of Brittany, whither he saith the soules of dead men are transported, doth perteine to this iland. For such a like tale is commonly told of Island.

A declaration of the Markes and Letters of this Mappe.

A. Is a fish which they commonly call Nahual. If any man eat of this fish, he dieth presently. It hath a tooth in the forepart of his head, standing out seuen cubites. This diuers haue sold for the Vnicornes horne. It is thought to be a good antidote and foueraigne medicine against poison. This Monster is forty elles in length. B. The Roider, a fish of an hundred and thirty elles in length, which hath no teeth. The flesh of it is very good meat, wholesome and toothsome. The fatte of it is good against many diseases. C. The Burchualur, hath his head bigger than all the body beside. It hath many very strong teeth, whereof they make Chesmen or Tablemen. It is threescore cubites long. D. The Hyena, the sea hogge, a monstrous kind of fish, of which thou maiest read in the 21. booke of Olaus Magnus. E. Ziphius, (it may be he meaneth Xiphius, the sword fish) an horrible sea monster, swallowing the blacke seale at one bitte. F. The English whale, thirty elles long: it hath no teeth, but the tongue of it is seuen elles in length. G. Hroshualur, that is as much to say as the Sea-horse, with a mane hanging downe from his necke like an horse. It often doth the fishermen great hurt and skare. H. The greatest kind of Whales, which seldome sheweth it selfe; it is more like a little iland, than a fish. It cannot follow or chase the smaller fishes, by reason of the huge greatnesse and waigth of his body, yet he praieth vpon many, which he catcheth by a naturall wile and subtilty which he vseth for to get his food. I. Skautuhvalur, this fish altogether full of gristles or bones; is somewhat like a ray or skaite but an infinite deale bigger: when it appeareth, it is like an iland, and with his finnes ouerturneth ships and boates. K. Seenaut, sea cowes, of colour gray: they sometimes come out of the sea and do feed vpon the land many in a company together. They haue a little bagge hanging at their nose, by the helpe of which they liue in the water: that being broken, they liue altogether vpon the land, and do accompany themselues with other kine. L. Steipereidur, a most gentle and tame kind of whale; which for the defence of the fishermen fighteth against other Whales. It is forbidden by Proclamation that no man may kill or hurt this sort of Whale. It is in length an hundred cubites at the least. M. Staukul, the Dutchmen call it Springual; he hath beene seene to stand a whole day together vpright vpon his taile. It is so called of leaping or skipping. It is a very dangerous enemy to seamen and fishers; and greedily seeketh after mans flesh. N. Rostunger, (which also is otherwise called a Rosmar,) is somewhat like a sea-calfe: it goeth in the bottome of the sea vpon foure feet, but very short ones. His skinne may scarcely be pearced with any weapon. Hee sleepeth twelue houres together hanging by his two long teeth vpon some rocke or cliffe. Ech of his teeth are at the least an elle long, but the length of his whole body is foureteen elles long. O. Spermaceti, parmacitty, or a base kind of amber, they commonly call it Hualambur. P. Blockes and Trunkes of tree by force of winde and violent tempest blowne vp by the the rootes from off the cliffes of Norway, tossed to and fro and passing through many stormes at length are cast vp, or do rest against this shore. Q. Huge and maruailous great heaps of ice brought hither with the tide from the frozen sea, making a great and terrible noise; some pieces of which oft times are fourty cubites bigge; vpon these in some places white beares do fitte closely, watching the silly fish which heere about do play and sport themselues.But I thinke it not amisse, to set downe the Verses of Erasmus Michaelis, which he hath of Island in his third booke De re Nautica.

In English thus:
Island a famous ile that’s farre remote and distant from the Maine,
North-west from hence doth lie in frozen sea: The countries chiefest gaine
Is Brimstone pale, which heere in mountaines high in plenty great is found;
Or heere and there like sand on shore li’th scattered on the ground.
The goodly pastures passing fatte, the lowly meddowes alwais green,
Such store of Neat and Kine in vales do feed, as else where may be seen.
The Sea on all sides round about, so many sundrie sorts of Fish
Doth yeeld, that none their names do know, or greater store may wish:
Whereof they daily lade great shippes from hence, and those away do send
To forrein countries euery way: though many things this ile commend,
For fish yet doth it farre excell all kingdomes of the world throughout,
By this the Nation grow’th in wealth, the people lusty strong and stout.
The Northern parts which lie full cold and bleake within the frozen zone,
Do breath forth flashing flames of fire, with lumpes of ashes, earth and stone.
Whot burning coals with filthy stinking smoke mount Hecla casteth out,
With hideous cracks and thundring noise, heard farre and neere about.

Certaine wordes expounded for the helpe of the Reader, and better vnderstanding of the Mappe.

Wic, that is, a creeke, inlet or bay. Jokul, a mountaine or hill. Ey, an ile: Eyer, ilands. Nes, the Dutch call it Nas and Nues, that is, a nose, a promontory or foreland shooting out into the sea. Lend, the Dutch pronounce it Landt, the land or earth. Clauster, a Cloister, or Monastery. Aust, the East; West, the place of the sunne setting; Nord, the North. Suyd, the South. Fior, signifieth foure.