Gaia stands for: Geometry, Algebra, Informatics and Application. The software consists in a set of Coq files that implement sets, groups, rings, etc. The objective is to implement the ”Elements of Mathematics” by N. Bourbaki. The files were originally written for Standard Coq; they are converted to ssreflect (version 1.3); the files have been compiled by Coq version 8.4.