Introduction
1. Global solutions to wave equations
existence theorems
2. L^p
L^q-decay estimates for the linear we equation
3. Linear symmetric hyperbolic systems
3.1 Energy estimates
3.2 A global existence theorem
3.3 Remarks on other methods
4. Some inequalities
5. Local existence for quasilinear symmetric hyperbolic
6. High energy estimates
7. Weighted a priori estimates
8. Global solutions to wave equations
proofs
8.1 Proof of Theorem 1.1
8.2 Proof ot Theorem 1.2
9. Other methods
10. Development of singularities
11. More evolutions equations
11.1 Equations of elasiticity
11.1.1 Initially isotropic media in R^3
11.1.2 Initially cubic media in R^3
11.2 Heat equations
11.3 Equations of thermoelasticity
11.4 Schrödinger equations
11.5 Klein-Gordon equations
11.6 Maxwell equations
11.7 Plate equations
12. Further aspects and questions
13. Evolution equations in waveguides
13.1 Nonlinear wave equations
13.1.1 Linear part
13.1.2 Nonlinear part
13.2. Schrödinger equations
13.3. Equations of elasticity and Maxwell equations
13.4 General waveguides
Appendix
A. Interpolation
B. The Theorem of Cauchy-Kowalevsky
C. A local existence theorem for hyperbolic-parabolic systems References Notation Index.