1 Motivation and perspective
Part I: Basic Functional Analysis and Calculus of Variations
2 A first exposure to Functional Analysis
3 Introduction to convex analysis. The Hahn-Banach and Lax-Milgram theorems
4 The Calculus of Variations for one-dimensional problems
Part II: Basic Operator Theory
5 Continuous operators
6 Compact operators
Part III: Multidimensional Sobolev Spaces and Scalar Variational Problems
7 Multidimensional Sobolev spaces
8 Variational problems
9 Finer results in Sobolev spaces and the Calculus of Variations
Appendix A: Hints and solutions to exercises
Appendix B: So much to learn.