This chapter from the book "Rearrangements and Convexity of Level Sets in PDE" by Bernhard Kawohl, published as Lecture Notes in Mathematics (1150) by Springer-Verlag, covers the following topics: 1. **Introduction**: Provides an overview of the content and purpose of the chapter. 2. **Rearrangements**: - A catalogue of rearrangements, which are techniques used to simplify or analyze partial differential equations (PDEs). 3. **Maximum Principles**: - The moving plane method, a technique used to prove maximum principles in PDEs. - Convexity of level sets, which discusses the properties of solutions to PDEs that are convex or concave. - Concavity or convexity of functions, exploring the behavior of solutions in terms of their convexity properties. The chapter also includes references, an index of examples and assumptions, and a subject index. The work is dedicated to the author's family and is subject to copyright restrictions.This chapter from the book "Rearrangements and Convexity of Level Sets in PDE" by Bernhard Kawohl, published as Lecture Notes in Mathematics (1150) by Springer-Verlag, covers the following topics: 1. **Introduction**: Provides an overview of the content and purpose of the chapter. 2. **Rearrangements**: - A catalogue of rearrangements, which are techniques used to simplify or analyze partial differential equations (PDEs). 3. **Maximum Principles**: - The moving plane method, a technique used to prove maximum principles in PDEs. - Convexity of level sets, which discusses the properties of solutions to PDEs that are convex or concave. - Concavity or convexity of functions, exploring the behavior of solutions in terms of their convexity properties. The chapter also includes references, an index of examples and assumptions, and a subject index. The work is dedicated to the author's family and is subject to copyright restrictions.