Differential Calculus.- Manifolds: The Basics.- From Local to Global.- Lie Groups.- Differential Forms.- Integration and Applications.- Cohomology and Degree Theory.- Euler-Poincare and Gauss-Bonnet.
Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.
"The book gives a detailed introduction to the world of differentiable manifolds and is of possible interested to everybody who wants to acquire a basic knowledge of differential geometry. ... Each chapter concludes with a list of exercises, solutions are given in the appendix." (Volker Branding, zbMATH 1338.58001, 2016)