Lecture Notes

1. Lecture Notes on Differential Geometry

These lecture notes are based on the lecture notes on Differential Geometry by Kirill Krasnov. These contain a semester’s worth of material and can be used hand in hand with other resources (see bibliography) to master the basics of Differential Geometry. The intended audience I have in mind consists of advanced undergraduates and beginning postgraduate students in physics and mathematics. I prioritize the more visual, physical perspective over the traditional definition-theorem-proof style of pure mathematics. Topics covered include: Manifolds, Vector Fields,  The Differential, Covectors, Immersions, Embeddings, Submanifolds, Tensors, Differential Forms, Integration of Differential Forms, The Metric, Lie derivative, Killing Vector Fields.