Calculus on Manifolds:

1. Manifolds, Tensor Analysis, and Applications, Second Edition. Ralph Abraham, Jerrold E. Marsden, and Tudor Ratiu, 1988, Springer-Verlag.
2. An Introduction to Differentiable Manifolds and Riemannian Geometry. William Boothby, 1986, Academic Press.
3. Calculus on Manifolds. A Modern Approach to Classical Theorems of Advanced Calculus. Michael Spivak, 1965, W. A. Benjamin, Inc.
4. Analysis on Manifolds. James R. Munkres, 1991, Addison-Wesley.

Basic Point-Set Topology and Analysis:

1. Topology. James R. Munkres, 2000, Prentice Hall.
2. Elementary Classical Analysis. Jerrold E. Marsden and Michael J. Hoffman, 1993, W. H. Freeman.

Algebraic Topology:

1. Elements of Algebraic Topology. James R. Munkres, 1984, Addison-Wesley.