Supplements

Notes by Donaldson: 

More notes by Donaldson:

Lecture by Donaldson 

27 lines on a cubic 

PDEs and isometric embeddings 

For background on manifolds and smooth maps, I suggest Guillemin/Pollack (Differerntial Topology, Chapter 1), or Lee (Riemannian Manifolds)

For a resource on PDE with Euclidean domains, I suggest Evans (Partial Differential Equations)