These are my lecture notes for the course on Differential Geometry for physics graduate students that I taught in Spring 2011. I have separated them into chapters – each chapter will contain notes from about one or two lectures.

• Chapter 1: Topology

• Chapter 2: Manifolds

• Chapter 3: Tangent vectors

• Chapter 4: Tangent space

• Chapter 5: Dual space

• Chapter 6: Vector fields

• Chapter 7: Pull back and push forward

• Chapter 8: Lie brackets

• Chapter 9: Lie algebra

• Chapter 10: Local flows

• Chapter 11: Lie derivative

• Chapter 12: Tensors

• Chapter 13: Differential forms

• Chapter 14: Exterior derivative

• Chapter 15: Volume form

• Chapter 16: Metric tensor

• Chapter 17: Hodge duality

• Chapter 18: Maxwell equations

• Chapter 19: Stokes' formula

• Chapter 20: Lie groups

• Chapter 21: Tangent space at the identity

• Chapter 22: One parameter subgroup

• Chapter 23: Fiber bundles

• Chapter 24: Connections

• Chapter 25: Curvature