Dr T is the man.
He was my phd advisor at @tufts. I strongly recommend his other textbooks, i.e. Differential forms in Algebraic topology, Differential Geometry.
A very nice textbook on manifolds. Must read, including De Rham theory, concise.
"An Introduction to Manifolds"
by
Loring W. Tu
Table of contents:
👉link.springer.com/book/10.10…