2015 version

Here is a developing set of lecture notes for a differential geometry course I've been putting together. The main theme of the course is to pursue differential geometry in the same spirit of the Guillemin and Pollack Differential Topology textbook. All our Riemann manifolds are submanifolds of Euclidean space (but with abstract Riemann metrics). We also use the iterated tangent bundles, and express Lie brackets, connections, torsion and the Riemann curvature tensor entirely in terms of iterated tangent bundles, the derivative as a bundle map, and the automorphism groups of iterated tangent bundles.

The March 25th, 2015 edition of the notes.