Lectures on Differential Equations and Differential Geometry (Classical Topics in Mathematics)

This book is superbly written by a world-leading expert on partial differential equations and differential geometry. It consists of two parts. Part I covers the existence and uniqueness of solutions of elliptic differential equations. It is direct, to the point, moves smoothly and quickly, and there are no unnecessary discussions or digressions. Many topics discussed in Part II will be new and surprising to many students, even to some experts in differential geometry. Both the selection of topics and the exposition are excellent. The detailed discussion of the case of surfaces motivated the later analogues in the higher dimensions.