TITLE: Munkres' Analysis on Manifolds and Differential Geometry
QUESTION [5 upvotes]: Will Munkres' Analysis on Manifolds prepare me for a text like John Lee's Introduction to Topological Manifolds and his Introduction to Smooth Manifolds text?
Would one be able to successfully tackle Spivak's Differential Geometry series after Munkres'?

REPLY [5 votes]: Analysis on Manifolds by Munkres is one of the finest books on the subject ever written, it is the subject matter for the second semester of Advanced Calculus at MIT. There are also lecture notes by Prof. Victor Guilleman available for download,  which supplement and improve the text. Go to ocw.mit.edu and find the Mathematics course 18.101, you will see in detail what is in the course. The book compares well with the second half advanced calculus by Loomis and Sternberg of Harvard University.  Yes, it will prepare you well for graduate courses in Manifolds. John Lee's book on smooth manifolds is good and well used. An alternative which I like is An Introduction to Differentiable Manifolds by William Boothby.