Preface.-1 Manifolds.-  2 Lie Derivatives.- 3 Differential Forms.- 4 Integral Manifolds.- 5 Connections .- 6. Riemannian Manifolds.- 7 Lie Groups.- 8 Hamiltonian Classical Mechanics.- References.-Index.

This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, and differential equations and a basic knowledge of analytical mechanics.

Gerardo Torres del Castillo has published two books previously, both in Birkhauser's Progress in Mathematical Physics series:
3-D Spinors, Spin-Weighted Functions and their Applications
, and
Spinors in Four-Dimensional Spaces
.