Manifolds tensors and forms : an introduction for mathematicians and physicists Providing a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology this books clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. The text covers the basics of multilinear algebra differentiation and integration on manifolds Lie groups and Lie algebras homotopy and de Rham cohomology homology vector bundles Riemannian and pseudo Riemannian geometry and degree theory. It also features over 250 detailed exercises and a variety of applications revealing fundamental connections to classical mechanics electromagnetism (including circuit theory) general relativity and gauge theory. Solutions to the problems are available for instructors at www.cambridge.org 9781107042193 Linear algebra Multilinear algebra Differentiation on manifolds Homotopy and de Rham cohomology Elementary homology theory Integration on manifolds Vector bundles Geometric manifolds The degree of a smooth map