Differential Geometry

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  • Geometry, Topology and Physics by M. Nakahara (2nd ed., IOP Publishing, 2003)Preparation for Gauge Theory by George Svetlichny math-ph/9902027
  • Algebraic Topology'' by Allen Hatcher (CUP, 2002) is downloadable from the webpage for the book


Allen Hatcher's website has his books on Algebraic Topology, Vector Bundles and K-Theory, Spectral Sequences in Algebraic Topology and 3-Manifolds.

Nigel Hitchin's Geometry of Surfaces course notes