1 Introduction. - 2 Instabilities and Patterns in Hydrodynamical Systems. - 2. 1 Rayleigh-Bénard instability. - 2. 2 Taylor-Couette instability. - 2. 3 Liquid crystal instabilities. - 3 Instabilities and Patterns in Reaction-Diffusion Systems. - 3. 1 Chemical instabilities. - 3. 2 Defect microstructures in irradiated materials. - 3. 3 Plastic deformation and dislocation patterns. - 4 Generic Aspects of Pattern-Forming Instabilities. - 4. 1 Phenomenology. - 4. 2 Reaction-diffusion dynamics and stability. - 4. 3 Reduced dynamics and amplitude equations. - 4. 4 Spatial patterns: selection and stability. - 4. 5 Phase dynamics of periodic patterns. - 5 The Hopf Bifurcation and Related Spatio-Temporal Patterns. - 5. 1 The generic aspects of oscillatory media. - 5. 2 Real chemical systems and the complex Ginzburg-Landau equation. - 5. 3 The effect of natural forcings on chemical oscillators. - 5. 4 Conclusions. - 6 The Turing Instability and Associated Spatial Structures. - 6. 1 The Turing mechanism. - 6. 2 The search for Turing structures. - 6. 3 At last genuine Turing structures?. - 6. 4 The interaction between Turing and Hopf instabilities. - 7 Defects and Defect Bifurcations. - 7. 1 Generic existence of defects. - 7. 2 Examples of defects. - 7. 3 Defects and disorder. - 7. 4 Bifurcation of defects. - 8 The Effect of External Fields. - 8. 1 Spatial forcing of stationary patterns. - 8. 2 Temporal forcing of a Hopf bifurcation. - 8. 3 Temporal forcing of one-dimensional wave patterns. - 8. 4 Temporal forcing of two-dimensional wave patterns. - 8. 5 Spatial forcing of wave patterns. - 8. 6 Flow field effects on pattern forming instabilities. - 8. 7 The effect of noise on wave patterns. - 8. 8 Conclusions. - 9 Fronts. - 9. 1 One-dimensional aspects. - 9. 2 Two-dimensional aspects. - 10 Pattern Formation: Generic versus Nongeneric Aspects. - 10. 1Kinetic coefficients. - 10. 2 Nongradient dynamics. - 10. 3 Experimental set-ups. - 11 Microstructures in Irradiated Materials. - 11. 1 Particle irradiation of metals and alloys. - 11. 2 Laser induced deformation of surfaces. - 12 Plastic Instabilities. - 12. 1 Dislocation dynamics and rate equations. - 12. 2 Stability analysis and bifurcations. - 12. 3 Nonlinear analysis. - 12. 4 Multiple slip. - 13 Afterword. - 14 Appendices. - 14. 1 Bifurcations and normal forms. - 14. 2 More about dynamical models. - 14. 3 The Brusselator: A toy model for pattern formation in RD systems. - 14. 4 Resonant forcings of nonlinear oscillators. Language: English