by Nigel Hitchin
This is an introductory course on differentiable manifolds. One of the historical driving forces of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. A large part of the text is occupied with the theory of differential forms and the exterior derivative.
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by John Morgan, Gang Tian - American Mathematical Society
This book provides full details of a complete proof of the Poincare Conjecture following Grigory Perelman's preprints. The book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology.
by Ana Cannas da Silva
The text covers foundations of symplectic geometry in a modern language. It describes symplectic manifolds and their transformations, and explains connections to topology and other geometries. It also covers hamiltonian fields and hamiltonian actions.
by Peter W. Michor - Birkhauser
This book is devoted to the theory of manifolds of differentiable mappings and contains result which can be proved without the help of a hard implicit function theorem of nuclear function spaces. All the necessary background is developed in detail.
by Bjorn Ian Dundas - Johns Hopkins University
This is an elementary text book for the civil engineering students with no prior background in point-set topology. This is a rather terse mathematical text, but provided with an abundant supply of examples and exercises with hints.