Partial Differential Equations, Vols. 13, appear in Springer’s Applied Math Sciences series, Vols. 115117. A second edition came out in 2011. This edition contains a number of additions and corrections, including seven new sections, given as follows.

 Volume 1: Chapter 4, Section 7; Chapter 6, Section 8.
 Volume 2: Chapter 7, Section 15; Chapter 10, Section 11.
 Volume 3: Chapter 13, Appendix A; Chapter 17, Sections 6 and 7.
A third edition appeared in 2023. It has the following new sections.
 Volume 1: Chapter 1, Section 18; Chapter 3, Appendices B and C; Chapter 6, Section 9.
 Volume 2: Chapter 7, Section 16; Chapter 8, Sections 8, 10, and 11, and Appendices A and B; Chapter 11, Section 11; Appendix C, Section 9.
 Volume 3: Chapter 14, Section 17; Chapter 17, Section 4.
Click on each volume to see what it has
 Volume 1 Partial Differential Equations I — Basic Theory
 Volume 2 Partial Differential Equations II — Qualitative Studies of Linear Equations
 Volume 3 Partial Differential Equations III — Nonlinear Equations
Click below to see a review of these three volumes by Peter Lax.