Introduction to Differentiable Manifolds

The first book to treat manifold theory at an introductory level, this text presents basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds. The final four chapters investigate the roles of differential structures in a variety of situations. 1963 edition.

Chapter 1.  Euclidean, Affine, and Differentiable Structure on Rn
Chapter 2.  Differentiable Manifolds
Chapter 3.  Projective Spaces and Projective Algebraic Varieties
Chapter 4.  The Tangent Bundle of a Differentiable Manifold
Chapter 5.  Submanifolds and Riemann Metrics
Chapter 6.  The Whitney Imbedding Theorem
Chapter 7.  Lie Groups and Their One-parameter Sub-groups
Chapter 8.  Integral Manifolds and Lie Subgroups
Chapter 9.  Fiber Bundles
Chapter 10.  Multilinear Algebra
References
Index