Armand Borel's mathematical work centered on the theory of Lie groups. Because of the increasingly important place of this theory in the whole of mathematics, Borel's work influenced some of the most important developments of contemporary mathematics. His first great achievement was to apply to Lie groups and homogenous spaces the powerful techniques of algebraic topology developed by Leray, Cartan, and Steenrod. In 1992, Borel was awarded the International Balzan Prize for Mathematics "for his fundamental contributions to the theory of Lie groups, algebraic groups and arithmetic groups, and for his indefatigable action in favor of high quality in mathematical research and of the propagation of new ideas."

He wrote more than 145 articles before 1982, which were collected in three volumes published in 1983. A fourth volume of subsequent articles was published in 2001. Volume I collects the papers written from 1948 to 1958.