INTRODUCTION 1. A Brief Introduction to Supercooled Liquids OVERVIEW 2. The Viscous-Liquid Glassy-Solid Problem THEORETICAL PERSPECTIVES ON SUPERCOOLED LIQUIDS 3. The Mode-Coupling Theory of the Glass Transition 4. Basic Physics of the Coupling Model: Direct Experimental Evidences 5. Frustration-Limited Domain Theory of Supercooled Liquids and the Glass Transition 6. Soft Modes in Glass-Forming Liquids: The Role of Local Stress 7. Entropic Approach to Relaxation Behavior in Glass-Forming Liquids 8. The Replica Approach to Glasses 9. Growing Length Scales in Supercooled Liquids 10. Shear Viscosity and Diffusion in Supercooled Liquids 11. Phase Separation in Silicate Melts: Limits of Solubilities EXPERIMENTAL ADVANCES IN SUPERCOOLED LIQUIDS 12. Higher Order Time-Correlation Functions from Fluctuating Energy Landscape Models: Comparison with Reduced Four-Dimensional NMR Spectroscopy 13. High-Frequency Dielectric Spectroscopy of Glass-Forming Liquids 14. Structural Relaxation of Supercooled Liquids from Impulsive Stimulated Light Scattering 15. Multiple Time Scales in the Nonpolar Solvation Dynamics of Supercooled Liquids POLYAMORPHISM AND SUPERCOOLED WATER 16. Polyamorphic Transitions in Network-Forming Liquids and Glasses 17. Facts and Speculation Concerning Low-Temperature Polymorphism in Glass Formers 18. Phase Diagram for Supercooled Water and Liquid-Liquid Transition 19. The Liquid-Liquid Critical-Point Hypothesis 20. Slow Dynamics in a Model and Real Supercooled Water 21. Raman Evidence for the Clathrate-like Structure of Highly Supercooled Water NOVEL APPLICATIONS: SUPERCOOLED LIQUIDS AND PROTEIN DYNAMICS 22. Cold Denaturation of Proteins 23. Vibrational Echo Studies of Heme-Protein Dynamics