I’ve finally gotten around to posting slides from a three-week lecture series I gave at Google a few months ago called Differential Geometry: Definitions and Pictures. The goal of the talk was to introduce the audience (mostly Google employees working in machine learning) to the way mathematicians think about the subject; there are lots of pictures and intuition and no proofs. The target audience has had a class in multivariable calculus and probably linear algebra.

As always when reading slides without seeing the talk, some parts might not make sense out of context, but I hope this can still be helpful to someone in its current state.