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Preface; 1: Introduction; Part 1; 2: Main applications; 3: Preliminaries and basic estimates; 4: Basic examples; 5: The Dirichlet problem I. Weak solutions; 6: The Dirichlet problem II. Limit solutions, very weak solutions and some other variants; 7: Continuity of local solutions; 8: The Dirichlet problem III. Strong solutions; 9: The Cauchy problem. L’ theory; 10: The PME as an abstract evolution equation. Semigroup approach; 11: The Neumann problem and problems on manifolds; Part 2; 12: The Cauchy problem with growing initial data; 13: Optimal existence theory for nonnegative solutions; 14: Propagation properties; 15: One-dimensional theory. Regularity and interfaces; 16: Full analysis of selfsimilarity; 17: Techniques of symmetrization and concentration; 18: Asymptotic behaviour I. The Cauchy problem; 19: Regularity and finer asymptotics in several dimensions; 20: Asymptotic behaviour II. Dirichlet and Neumann problems; Complements; 21: Further applications; 22: Basic facts and appendices; Bibliography; Index

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