1 Generation and Representation. - 1. 1 Uniformly Continuous Semigroups of Bounded Linear Operators. - 1. 2 Strongly Continuous Semigroups of Bounded Linear Operators. - 1. 3 The Hille-Yosida Theorem. - 1. 4 The Lumer Phillips Theorem. - 1. 5 The Characterization of the Infinitesimal Generators of C0 Semigroups. - 1. 6 Groups of Bounded Operators. - 1. 7 The Inversion of the Laplace Transform. - 1. 8 Two Exponential Formulas. - 1. 9 Pseudo Resolvents. - 1. 10 The Dual Semigroup. - 2 Spectral Properties and Regularity. - 2. 1 Weak Equals Strong. - 2. 2 Spectral Mapping Theorems. - 2. 3 Semigroups of Compact Operators. - 2. 4 Differentiability. - 2. 5 Analytic Semigroups. - 2. 6 Fractional Powers of Closed Operators. - 3 Perturbations and Approximations. - 3. 1 Perturbations by Bounded Linear Operators. - 3. 2 Perturbations of Infinitesimal Generators of Analytic Semigroups. - 3. 3 Perturbations of Infinitesimal Generators of Contraction Semigroups. - 3. 4 The Trotter Approximation Theorem. - 3. 5 A General Representation Theorem. - 3. 6 Approximation by Discrete Semigroups. - 4 The Abstract Cauchy Problem. - 4. 1 The Homogeneous Initial Value Problem. - 4. 2 The Inhomogeneous Initial Value Problem. - 4. 3 Regularity of Mild Solutions for Analytic Semigroups. - 4. 4 Asymptotic Behavior of Solutions. - 4. 5 Invariant and Admissible Subspaces. - 5 Evolution Equations. - 5. 1 Evolution Systems. - 5. 2 Stable Families of Generators. - 5. 3 An Evolution System in the Hyperbolic Case. - 5. 4 Regular Solutions in the Hyperbolic Case. - 5. 5 The Inhomogeneous Equation in the Hyperbolic Case. - 5. 6 An Evolution System for the Parabolic Initial Value Problem. - 5. 7 The Inhomogeneous Equation in the Parabolic Case. - 5. 8 Asymptotic Behavior of Solutions in the Parabolic Case. - 6 Some Nonlinear Evolution Equations. - 6. 1 Lipschitz Perturbations of LinearEvolution Equations. - 6. 2 Semilinear Equations with Compact Semigroups. - 6. 3 Semilinear Equations with Analytic Semigroups. - 6. 4 A Quasilinear Equation of Evolution. - 7 Applications to Partial Differential EquationsLinear Equations. - 7. 1 Introduction. - 7. 2 Parabolic EquationsL2 Theory. - 7. 3 Parabolic EquationsLp Theory. - 7. 4 The Wave Equation. - 7. 5 A Schrödinger Equation. - 7. 6 A Parabolic Evolution Equation. - 8 Applications to Partial Differential EquationsNonlinear Equations. - 8. 1 A Nonlinear Schröinger Equation. - 8. 2 A Nonlinear Heat Equation in R1. - 8. 3 A Semilinear Evolution Equation in R3. - 8. 4 A General Class of Semilinear Initial Value Problems. - 8. 5 The Korteweg-de Vries Equation. - Bibliographical Notes and Remarks. Language: English