I want to start studying differential geometry but I can't seem to find a proper starting path. Whenever I try to search for differential geometry books/articles I get a huge list. I know that it is a broad topic, but I want some advice for you regarding the books and articles. I want to learn differential geometry and especially manifolds. I have some background in abstract algebra, linear algebra, topology, real/complex analysis.
M. Spivak, A comprehensive introduction to differential geometry, Publish or Perish, Wilmington, DL, 1979 is a very nice, readable book.
If you prefer something shorter, there are two books of M. Do Carmo, 1. Differential geometry of curves and surfaces, and 2. Riemannian geometry.
I'm studying differential geometry in order to learn general relativity. My advisor recommended the following book: Semi-Riemannian Geometry, With Applications to Relativity, by Barrett O'Neill.