I recently gave a series of lectures on the geometry and analysis of black holes in general relativity, as part of the Nachdiplom series, at ETH Zürich. Lecture notes (under construction!) are available here (last updated December 18, 2013).

In Michaelmas 2012, I lectured Part III Differential Geometry. A set of lecture notes–under construction–are available here. Example classes are being run by Gabriele Benedetti and Giulio Codogni who maintain a webpage with the example sheets and helpful comments.

In Michaelmas 2010 and 2011, I lectured Partial Differential Equations in the Cambridge Centre for Analysis. Course materials are available (to CCA students) here. Willie Wong has written some supplementary notes on Sobolev spaces, and Stefanos Aretakis has written some notes on the geometric approach to the analysis of the wave equation, available here and here.

I have also written a set of lecture notes for Part II Linear Analysis, which can be accessed here.

I have given several summer school courses on wave equations on black holes, at Krakow (September 2010), Aarhus (July 2010), IHES (July 2010), and–jointly with Igor Rodnianski–in Zürich (July 2008). The latter course gave rise to these lecture notes, to be published by the Clay Mathematics Institute.

Some unfinished lecture notes accompanying a short course I gave at MIT in the Fall of 2007 on the geometry and analysis of black hole spacetimes can be accessed here.

A set of slides from a short non-examinable course I gave in Lent 2005 can be found here.