Geometry in Physics
by Alexander Altland
Number of pages: 79
From the table of contents: Exterior Calculus (Exterior Algebra, Differential forms in Rn, Metric, Gauge theory, Summary and outlook); Manifolds (Basic structures, Tangent space, Summary and outlook); Lie groups (Generalities, Lie group actions, Lie algebras, Lie algebra actions, From Lie algebras to Lie groups).
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by Giovanni Landi - arXiv
These lectures notes are an introduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists.
by Christopher Pope - Texas A&M University
Lecture notes on Geometry and Group Theory. In this course, we develop the basic notions of Manifolds and Geometry, with applications in physics, and also we develop the basic notions of the theory of Lie Groups, and their applications in physics.
by Ingemar Bengtsson - Stockholms universitet, Fysikum
These are the lecture notes from a graduate course in the geometry of quantum mechanics. The idea was to introduce the mathematics in its own right, but not to introduce anything that is not directly relevant to the subject.
by Alain Connes - Academic Press
The definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics. Ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics.