1. Introduction;
Part- I. Representation Formulas for Solutions;
2. Four Important Linear PDE;
3. Nonlinear First-Order PDE;
4. Other Ways to Represent Solutions;
Part- II. Theory for Linear Partial Differential Equations;
5. Sobolev Spaces;
6. Second-Order Elliptic Equations;
7. Linear Evolution Equations;
Part-III. Theory for Nonlinear Partial Differential Equations;
8. The Calculus of Variations;
9. Nonvariational Techniques;
10. Hamilton Jacobi Equations;
11. Systems of Conservation Laws
Appendix A: Notation;
Appendix B: Inequalities;
Appendix C: Calculus Facts;
Appendix D: Linear Functional Analysis;
Appendix E: Measure Theory;
Bibliography;
Index

Lawrence C. Evans presents a comprehensive survey of modern techniques in the theoretical study of partial differential equations, with particular emphasis on nonlinear equations