A 33 page lecture from Oxford on the uses of geometry in physics.

This is a WWW textbook written by Evans M. Harrell II and James V. Herod, both of Georgia Tech. It is suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations. Students are expected to have completed two years of calculus and an introduction to ordinary differential equations and vector spaces. Topics include Fourier series, Green's functions, and PDEs.

Covers Conformal Field Theory, Modular Functor, Topological Quantum Field Theory and Frobenius Algebras, Operads, Homotyopy Algebra.

A text on the mathematics needed for upper level undergraduate physics courses by James Nearing, University of Miami (PDF).

Covers Complex variables, special functions, second order linear ODEs, asymptotic expansions, Laplace transforms. (One large PS file)

A set of lecture notes for this one semester course.

Class lecture notes at a graduate level on the mathematical background needed to understand classical gauge theory.

A fourth year math/physics course at UIUC with online lecture notes.