GAP was developed at Lehrstuhl D für Mathematik (LDFM), Rheinisch-Westfälische Technische Hochschule Aachen, Germany from 1986 to 1997.

After the retirement of Joachim Neubüser from the chair of LDFM, the development and maintenance of GAP was coordinated by the School of Mathematical and Computational Sciences at the University of St Andrews, Scotland.

[2] In the summer of 2005 coordination was transferred to an equal partnership of four 'GAP Centres', located at the University of St Andrews, RWTH Aachen, Technische Universität Braunschweig, and Colorado State University at Fort Collins; in April 2020, a fifth GAP Centre located at the TU Kaiserslautern was added.

[3] GAP contains a procedural programming language and a large collection of functions to create and manipulate various mathematical objects.

The user contributed packages are an important feature of the system, adding a great deal of functionality.