1. Introduction.- 2. Wave Motion.- 2.1 What is Wave Motion?.- 2.2 Dispersive and Nonlinear Effects of a Wave.- 2.3 Solitary Waves and the Korteweg de Vries Equation.- 2.4 Solution of the Korteweg de Vries Equation.- 3. Lightwave in Fibers.- 3.1 Polarization Effects.- 3.2 Plane Electromagnetic Waves in Dielectric Materials.- 3.3 Kerr Effect and Kerr Coefficient.- 3.4 Dielectric Waveguides.- 4. Information Transfer in Optical Fibers and Evolution of the Lightwave Packet.- 4.1 How Information is Coded in a Lightwave.- 4.2 How Information is Transferred in Optical Fibers.- 4.3 Master Equation for Information Transfer in Optical Fibers: The Nonlinear Schrodinger Equation.- 4.4 Evolution of the Wave Packet Due to the Group Velocity Dispersion.- 4.5 Evolution of the Wave Packet Due to the Nonlinearity.- 4.6 Technical Data of Dispersion and Nonlinearity in a Real Optical Fiber.- 4.7 Nonlinear Schrodinger Equation and a Solitary Wave Solution.- 4.8 Modulational Instability.- 4.9 Induced Modulational Instability.- 4.10 Modulational Instability Described by the Wave Kinetic Equation.- 5. Optical Solitons in Fibers.- 5.1 Soliton Solutions and the Results of Inverse Scattering.- 5.2 Soliton Periods.- 5.3 Conservation Quantities of the Nonlinear Schrodinger Equation.- 5.4 Dark Solitons.- 5.5 Soliton Perturbation Theory.- 5.6 Effect of Fiber Loss.- 5.7 Effect of the Waveguide Property of a Fiber.- 5.8 Condition of Generation of a Soliton in Optical Fibers.- 5.9 First Experiments on Generation of Optical Solitons.- 6. All-Optical Soliton Transmission Systems.- 6.1 Raman Amplification and Reshaping of Optical Solitons-First Concept of All-Optical Transmission Systems.- 6.2 First Experiments of Soliton Reshaping and of Long Distance Transmission by Raman Amplifications.- 6.3 First Experiment of Soliton Transmission by Means of an Erbium Doped Fiber Amplifier.- 6.4 Concept of the Guiding Center Soliton.- 6.5 The Gordon-Haus Effect and Soliton Timing Jitter.- 6.6 Interaction Between Two Adjacent Solitons.- 6.7 Interaction Between Two Solitons in Different Wavelength Channels.- 7. Control of Optical Solitons.- 7.1 Frequency-Domain Control.- 7.2 Time-Domain Control.- 7.3 Control by Means of Nonlinear Gain.- 7.4 Numerical Examples of Soliton Transmission Control.- 8. Influence of Higher-Order Terms.- 8.1 Self-Frequency Shift of a Soliton Produced by Induced Raman Scattering.- 8.2 Fission of Solitons Produced by Self-Induced Raman Scattering.- 8.3 Effects of Other Higher-Order Dispersion.- 9. Polarization Effects.- 9.1 Fiber Birefringence and Coupled Nonlinear Schrodinger Equations.- 9.2 Solitons in Fibers with Constant Birefringence.- 9.3 Polarization-Mode Dispersion.- 9.4 Solitons in Fibers with Randomly Varying Birefringence.- 10. Dispersion-Managed Solitons (DMS).- 10.1 Problems in Conventional Soliton Transmission.- 10.2 Dispersion Management with Dispersion-Decreasing Fibers.- 10.3 Dispersion Management with Dispersion Compensation.- 10.4 Quasi Solitons.- 11. Application of Dispersion Managed Solitons for Single-Channel Ultra-High Speed Transmissions.- 11.1 Enhancement of Pulse Energy.- 11.2 Reduction of Gordon-Haus Timing Jitter.- 11.3 Interaction Between Adjacent Pulses.- 11.4 Dense Dispersion Management.- 11.5 Nonstationary RZ Pulse Propagation.- 11.6 Some Recent Experiments.- 12. Application of Dispersion Managed Solitons for WDM Transmission.- 12.1 Frequency Shift Induced by Collisions Between DM Solitons in Different Channels.- 12.2 Temporal Shift Induced by Collisions Between DM Solitons in Different Channels.- 12.3 Doubly Periodic Dispersion Management.- 12.4 Some Recent WDM Experiments Using DM Solitons.- 13. Other Applications of Optical Solitons.- 13.1 Soliton Laser.- 13.2 Pulse Compression.- 13.3 All-Optical Switching.- 13.4 Solitons in Fibers with Gratings.- 13.5 Solitons in Microstructure Optical Fibers.- References.