Editio Princeps= First published Edition

The first major work to be printed on Gutenberg’s press was a magnificent edition of the Latin (Vulgate) Bible.

The first Western scholar to conceive the idea of producing a version of the Greek New Testament was a Spanish cardinal named Ximenes de Cisneros (1437–1517). Under his leadership, a group of scholars, including one named Diego Lopez de Zuñiga (Stunica), undertook a multivolume edition of the Bible.

The work was printed in a town called Alcalá, whose Latin name is Complutum. For this reason, Ximenes’s edition is known as the Complutensian Polyglot. 

The 5 volume work by completed by 1514 however due to some complications it wasn't published until 1522.

During this time Erasmus  was persuaded by a publisher named Johann Froben to produce and publish a Greek New Testament.

And so both of these men hastened and the printing of Erasmus’s edition began in October 1515 and was finished in just five months. The edition included the rather hastily gathered Greek text and a revised version of the Latin Vulgate, side by side (in the second and later editions, Erasmus included his own Latin translation of the text in lieu of the Vulgate.

So Erasmus' edition was the first published Greek New Testament.

Textus Receptus:

The common phrase Textus

Receptus (abbreviated T.R.), a term used by textual critics to refer to that form of the Greek text that is based, not on the oldest and best manuscripts, but on the form of text originally published by Erasmus

and handed down to printers for more than three hundred years, until textual scholars began insisting that the Greek New Testament should be established on scientific principles based on our oldest and best manuscripts, not simply reprinted according to custom. It was the inferior textual form of the Textus Receptus that stood at the base of the earliest English translations, including the King James Bible, and other editions until near the end of the nineteenth century.

Source: Misquoting Jesus-Bart Ehrman.