Free textbooks in geometry

Combinatorial Geometry

• The Geometry Junkyard Usenet clippings, web pointers, lecture notes, research excerpts, papers, abstracts, programs, problems, and other stuff (by Prof. David Eppstein)
• Geometry in Action by Prof. David Eppstein.

Differential Geometry

Introduction to Tensor Calculus and Continuum Mechanics, by John H. Heinbockel
• Topics in Differential Geometry, Peter W. Michor.
• Intrinsic Geometry of Surfaces by A. D. Aleksandrov and V. A. Zalgaller
• Riemann Surfaces, Dynamics and Geometry Curtis McMullen
• Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem by Peter B. Gilkey
• Differentiable Manifolds lecture notes (growing) by Mariusz Wodzicki
• Lecture notes for the course in Differential Geometry by Sergei Yakovenko
• Differential Geometry lecture notes by Gabriel Lugo
• Differential geometry reconstructed by Alan U. Kennington
• Course of Differential Geometry by Ruslan Sharipov
• A Modern Course on Curves and Surfaces by Richard S. Palais
• Twistor Geometry and Gauge Theory by Martin Wolf
• Complex Geometry of Nature and General Relativity by Giampiero Esposito