chapter Introduction. Some Definitions, Formulas, Methods, and Solutions -- chapter 1 Parabolic Equations with One Space Variable -- chapter 2 Parabolic Equations with Two Space Variables -- chapter 3 Parabolic Equations with Three or More Space Variables -- chapter 4 Hyperbolic Equations with One Space Variable -- chapter 5 Hyperbolic Equations with Two Space Variables -- chapter 6 Hyperbolic Equations with Three or More Space Variables -- chapter 7 Elliptic Equations with Two Space Variables -- chapter 8 Elliptic Equations with Three or More Space Variables -- chapter 9 Higher-Order Partial Differential Equations.