Textbooks
The main textbook for the course is:
Introduction to smooth manifolds by John M. Lee (2nd ed). (Buy a hard copy here)
We will also use material from these books:
An Introduction to Manifolds, by Loring Tu
Differential Topology by V. Guillemin and A. Pollack.
These are available in this Textbook Folder along with the following additional textbooks which cover much the same material.
An Introduction to Differentiable Manifolds and Riemannian Geometry by W.M. Boothby
Calculus On Manifolds by Michael Spivak, a good reference on Real Analysis in several variables.
Foundations of Differentiable Manifolds and Lie Groups by Frank Warner.
Topology from the Differentiable Viewpoint by John Milnor
Morse Theory by John Milnor.
An Introduction to Differential Manifolds by Jacques Lafontaine
Topology by J. Munkres, 2nd edition (a great reference for point set topology)