[pdf] An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces Second Edition (Theoretical and Mathematical Physics) Martin Schlichenmaier

This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.