Description: An Introduction to Manifolds presents the theory of manifolds with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book, the reader will have the ability to compute one of the most basic topological invariants of a manifold, its de Rham cohomology.
Review Quotes:
From the reviews of the second edition:
"This book could be called a prequel to the book 'Differential forms in algebraic topology' by R. Bott and the author. Assuming only basic background in analysis and algebra, the book offers a rather gentle introduction to smooth manifolds and differential forms offering the necessary background to understand and compute deRham cohomology. ... The text also contains many exercises ... for the ambitious reader." (A. Cap, Monatshefte für Mathematik, Vol. 161 (3), October, 2010)