Equivariant cohomology on smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Br ning and V.W. Guillemin. The point of departure are two relatively short but very remarkable papers be Henry Cartan, published in 1950 in the Proceedings of the "Colloque de Topologie". These papers are reproduced here, together with a modern introduction to the subject, written by two of the leading experts in the field...