I. The Two Basic Blowup Mechanisms. - A. The ODE mechanism. - B. The geometric blowup mechanism. - C. Combinations of the two mechanisms. - Notes. - II. First Concepts on Global Cauchy Problems. - 1. Short time existence. - 2. Lifespan and blowup criterion. - 3. Blowup or not? Functional methods. - 4. Blowup or not? Comparison and averaging methods. - Notes. - III. Semilinear Wave Equations. - 1. Semilinear blowup criteria. - 2. Maximal influence domain. - 3. Maximal influence domains for weak solutions. - 4. Blowup rates at the boundary of the maximal influence domain. - 5. An example of a sharp estimate of the lifespan. - Notes. - IV. Quasilinear Systems in One Space Dimension. - 1. The scalar case. - 2. Riemann invariants simple waves and L1-boundedness. - 3. The case of 2 × 2 systems. - 4. General systems with small data. - 5. Rotationally invariant wave equations. - Notes. - V. Nonlinear Geometrical Optics and Applications. - 1. Quasilinear systems in one space dimension. - 2. Quasilinear wave equations. - 3. Further results on the wave equation. - Notes. Language: English