1 Introduction 1.1 Traditional Nonlinear Optics-Extreme Nonlinear Optics 1.2 How to Read this Book? 2 Selected Aspects of Few-Cycle Laser Pulses and Nonlinear Optics 2.1 Maxwell Equations 2.2 The Light Intensity 2.3 Electric Field in a Laser Resonator 2.4 A Brief Look at Phenomenological Nonlinear Optics 2.5 Even-Harmonic Generation and Inversion Symmetry 2.6 Principle of Measuring the Carrier-Envelope Frequency 3 The Lorentz Oscillator Model and Beyond 3.1 Linear Optics:Revisiting the Lorentz Oscillator Model 3.2 Two-Level Systems and Rabi Energy 3.3 Carrier-Wave Rabi Flopping 3.4 Frequency Doubling with Inversion Symmetry 3.5 Quantum Interference of Multiphoton Absorption 3.6 High Harmonics from Two-Level Systems 3.6.1 The 'Static-Field Approximation' 3.6.2 The 'Square-Wave Approximation' 3.6.3 The Dressed Two-Level System:Floquet States 4 The Drude Free-Electron Model and Beyond 4.1 Linear Optics:The Drude Model 4.2 Electron Wave Packets Driven by Light 4.2.1 Semiclassical Considerations 4.2.2 Quantum-Mechanical Treatment:Dressed Electrons 4.3 Crystal Electrons 4.3.1 Static-Field Case 4.3.2 High Harmonics from Carrier-Wave Bloch Oscillations 4.4 Extreme Nonlinear Optics of Relativistic Electrons 4.4.1 Second-Harmonic Generation and Photon Drag 4.4.2 Nonperturbative Regime 4.5 Extreme Nonlinear Optics of Dirac Electrons 4.6 Unruh Radiation 5 Lorentz Becomes Drude:Bound-Unbound Transitions 5.1 High-Harmonic Generation:Phenomenological Approach 5.2 The Keldysh Parameter 5.3 Field Ionization of Atoms 5.4 High-Harmonic Generation 5.4.1 Three-Step Scenario and Cutoff 5.5 Application to Photoemission from Metal Surfaces 6 Accounting for Propagation Effects 6.1 Numerical Solution of the Nonlinear Maxwell Equations 6.2 Slowly Varying Envelope Approximation 6.3 Gouy Phase and Carrier-Envelope Phase 6.4 Reshaping of the Amplitude Spectrum 7 Extreme Nonlinear Optics of Semiconductors and Isolators 7.1 Carrier-Wave Rabi Flopping 7.1.1 Experiment 7.1.2 Theory 7.1.3 Dependence on the Carrier-Envelope Phase 7.1.4 SemiconductorBloch Equations 7.2 'THG in the Disguise of SHG' 7.3 Dynamic Franz-Keldysh Effect 7.4 Photon Drag or Dynamic Hall Effect 7.5 Conical Second-Harmonic Generation 8 Extreme Nonlinear Optics of Atoms and Electrons 8.1 High-Harmonic Generation From Atoms 8.1.1 Gas Jets 8.1.2 Hollow Waveguides 8.1.3 Quasi Phase-Matching in Modulated Capillaries 8.1.4 Dependence on the Carrier-Envelope Phase 8.2 Relativistic Nonlinear Thomson Scattering Solutions Symbols References Index