, 2 2 differential ideal 3 Bourbaki Elements de mathematique de Rham 4, 5 , de Rham cohomology singular cohomology graded algebra , graded algebra , graded group Warner , graded algebra , 6 , de Rham Hodge ,. This is my first and my last kindle edition purchase The book was traslated without any care about mathematical notations The paper edition is fine, kindle edition is very very bad. If you are looking for a great reference for differentiable manifolds this is it Be careful though it is dense at times. This is an incredible textbook Great for graduate students who have taken a course in vector calculus of differentiable topology Not heavy on structure theorems or representation theory but fantastic for basics of Lie groups. Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem Very well job done. It s a classic book A reference in Lie groups.