Abraham Ortelius; 1528-1598.

Ortelius' name is often associated with Ptolemy and Mercator, when evocating the founding fathers of cartography. Abaham Ortel (Ortelius), born in Antwerp, trained in classics and math.
He became a book dealer and a map colorist. Widely traveling to attend fairs, he befriended many literati, in his homeland and abroad. Upon their encouragement, he engaged in 1570 in the "Theatrum Orbis Terrarum" project, by collecting maps, charts and plans among diverse cartographers, and having Frans Hogenberg* re-engrave them in the same uniform size and style, to form the first known modern Atlas (even though this term was not used for another twenty years by his major competitor: Gerard Mercator!).
The Theatrum knew an immediate and lasting success, being re-issued many times over in different languages. It always gave credit to the sources of informations and other contributors used to produce the maps (a practice few followed in those days).
Of note: the 42 editions of the "Theatrum" between 1570 and 1612, the 1577 "Spiegel der Werelt" (reduced version of the Theatrum engraved by Philippe Galle, issued till 1585); and the 1579 "Parergon Theatri" (historical atlas, reissued till 1624).
*Hogenberg associated with Georg Braun, was famous for their 1572 "Civitates Orbis Terrarum", a compilation of plans of the most significant towns of the time, being recycled many times till 1750 by Abraham Hogenberg, Frederick de Wit, Pieter van der Aa, and Covens & Mortier.

La Florida.

This relatively small map (8 ¾" X 6"), drawn by Geronimo de Chaves (see credit given in the cartouche) of the Casa de Contratacion of Sevilla, was first printed in 1584 as an inset on a larger map for the Additamentum III of the "Theatrum Orbis Terrarum". The large composition map is made up of three insets: (top right) coast of Florida, (bottom right) coast of Texas/Mexico, (left) coast of Panama/Colombia/Ecuador/Peru. This why this Florida map, having been cut away, has been re-margined on the left side and on the bottom side.
Examination of the text on verso leads to conclude this specific item was printed for the 1595 Latin edition of the Theatrum (see Cartographia Neerlandica, ref. 15b).
The map takes into account Hernando de Soto discoveries during his ill-fated expedition of 1539-1543 In particular, it is one of the first maps to show some progress in the delineation of the coast and the course of major rivers (see the Mississippi called here Rio del Spirito Sancto).
The towns shown inland are probably main indian tribe sites which de Soto put to porter duty contribution during his tribulations.
Of note: in present day Alabama, and quite properly located, the "Tascalisa" township is quite reminiscent of Tuscaloosa, .
But it does not show the discoveries made by the French explorers and colonists (namely in South Ca rolina, and specially around the Saint John River where the very first French colony on US soil was established by René Goulaine de Laudonière in 1564). Neither does it mention Saint Augustine (first buit by Pedro Menendez de Aviles in 1565, as the Spanish base of attack against the French settlement).
Fascinating detail: on the Florida Atlantic coast, the "Cabo de Cañareal" (may be named after the presence of (sugar?) canes), gives a hint to the origins of the name of present day Cape Canaveral. Latin text on verso.