1. Some basic mathematics
2. Differentiable manifolds and tensors
3. Lie derivatives and Lie groups
4. Differential forms
5. Applications in physics
6. Connections for Riemannian manifolds and gauge theories

"In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory."