I will be lecturing at this graduate summer school in Nairobi, see the workshop website. It will take place at the School of Mathematics, Chiromo Campus, University of Nairobi. The organizers are Jared Ongaro, University of Nairobi, and Balazs Szendroi, University of Oxford. My PhD student Jacob Gross will be helping out with some teaching at the school. We would like to gratefully acknowledge funding from the Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Denmark, which came from the Danish National Research Foundation. Professor Miles Reid of Warwick University will also be lecturing, on topics in Algebraic Geometry.
I intend to give two lecture courses, first one on "Introduction to Differential Geometry", and then one on "Complex manifolds and Kähler geometry". I don't know how much time we will have, so the second lecture course may not get very far. You can find more details and course materials, including PDF slides of the lectures, at the following links:
Introduction to Differential Geometry
Complex manifolds and Kähler geometry
The material on these pages is adapted versions of two graduate lecture courses I gave in Oxford, plus a selection of useful references, problem sheets, miniprojects, and so on. In fact there is far too much material for me to get through in a week -- we will be lucky if I cover more than 50% of what's there. But I am including everything to help people that want to to learn more later, or even give a lecture course on the material themselves in their home university.
Homework question sheet: Homework 1.