Partha Niyogi's very lucid talk entitled Geometric Methods and Manifold Learning includes a brief and very basic introduction to differential geometry(starts at t=40:49) which I found helpful.
This was part of the Machine Learning Workshop I attended at the University of Chicago last June (MLSS'09). There were several other talks and tutorials of note. I especially enjoyed Emmanuel Candes' talk on sparse signal recovery. The talks are available at the videolectures website.