I. Evolution Equations on ?n. - 1. The Space ?n. - 2. Evolution Equations on ?n. - 3. Finite Escape Times. - 4. Processes on ?sun X ?. - 5. Linear Dynamical Systems. - 6. The Simplest Class of Processes. - 7. Stability of a Particular Motion: Processes. - 8. Stability of Equilibrium: Dynamical Systems. - 9. Stability of Equilibrium: Linear Dynamical Systems. - 10. Quadratic Liapunov Functions and Linearization. - 11. The Invariance Principle and Asymptotic Behavior. - 12. Comments and Extensions. - References. - II. Preliminaries for Abstract Evolution Equations. - 1. Abstract Spaces. - 2. Functions. - 3. Linear Functions. - 4. Differentiation of Functions. - 5. Abstract Evolution Equations. - References. - III. Abstract Dynamical Systems and Evolution Equations. - 1. Dynamical Systems and C0-Semigroups. - 2. Linear Dynamical Systems. - 3. Generation of Linear Dynamical Systems. - 4. Choosing the State Space in Applications. - 5. Generation of Nonlinear Dynamical Systems. - 6. Comments and Extensions. - References. - IV. Some Topological Dynamics. - 1. Liapunov Functions and Positive Invariance. - 2. Computation of V. - 3. Stability and Liapunov's Direct Method. - 4. Positive Limit Sets and the Invariance Principle. - 5. Orbital Precompactness and Use of the Invariance Principle. - 6. Comments and Extensions. - References. - V. Applications and Special Topics. - 1. A Feedback Control Problem. - 2. The Thermoelastic Stability Problem. - 3. The Viscoelastic Stability Problem. - 4. A Fission Reactor Stability Problem. - 5. A Supersonic Panel-Flutter Problem. - 6. Discrete Dynamical Systems. - 7. Finite-Dimensional Approximation. - References. Language: English