This post-holocaust game takes place in a far future world, where technology, psionics, mutations, and radiation interplay and mix in a ruined world that has returned to the wilds.
Likely sources of inspiration for this game include Road Warrior, the Hanna-Barbera cartoon Thundarr the Barbarian, Alien, and uncountable numbers of sci-fi / post-holocaust films of the 1950s, 1960s, and 1970s. It also descended from the earlier TSR game Metamorphosis Alpha, which involved the mutated crew of a generation starship named Warden. A component of this starship appears in the old Dungeons & Dragons module Expedition to the Barrier Peaks.
The original mechanics are similar in many respects to the original D&D game system, although the second and third editions changed things substantially. In particular, the third edition resembled TSR's Marvel Super Heroes.
The Fourth Edition was closer to 2nd edition Advanced Dungeons and Dragons (AD&D), and a number of design advancements for 4th Edition formed the basis of several new design elements of Third Edition D&D.
The Fifth Edition http://www.wizards.com/gammaworld/ was based on TSRs Alternity system - a system which was canceled a month before the Gamma World book was released!
In late 2003 Sword and Sorcery (A White Wolf label) released a new edition of Gamma World. This edition uses the D20 system abstracted from the 3rd Edition of Dungeons and Dragons and requires books either from that line or the related D20 Modern line to be used. It's backward compatibility with earlier editions varies, with first (being a close relative of the earliest D&D) and fourth (being a relative of 2nd edition D&D and a source of inspiration for 3rd edition) would probably be the easiest to translate material between.