This is essentially a reprint of the authors’ well-known book (originally published by Prentice-Hall) (1967; Zbl 0153.13602). The structure of the volume is unchanged. After a preface, there is an introductory chapter on the one-dimensional maximum principle, followed by three other parts on maximum principles for elliptic, parabolic, and hyperbolic operators. Chapter 1 contains 9 sections, Chapter 2 is divided into 16 sections, while the following two chapters contain 8, and respectively 11 sections. Each section ends with pedagogically chosen exercises, while at the end of each chapter a bibliographical discussion is included.
Though a long time passed since the book was first published, it is still of great value for advanced undergraduate and graduate students, as well as for investigators and users of partial differential equations in mathematics, physics, engineering, and related sciences.