Introduction Historical Overview--Compositions Historical Overview--Words A More Detailed Look Basic Tools of the Trade Sequences Solving Recurrence Relations Generating Functions Compositions Definitions and Basic Results (One Variable) Restricted Compositions Compositions with Restricted Parts Connection between Compositions and Tilings Colored Compositions and Other Variations Research Directions and Open Problems Statistics on Compositions History and Connections Subword Patterns of Length 2: Rises, Levels, and Drops Longer Subword Patterns Research Directions and Open Problems Avoidance of Non-Subword Patterns in Compositions History and Connections Avoidance of Subsequence Patterns Generalized Patterns and Compositions Partially Ordered Patterns in Compositions Research Directions and Open Problems Words History and Connections Definitions and Basic Results Subword Patterns Subsequence Patterns--Classification Subsequence Patterns--Generating Functions Generalized Patterns of Type (2,1) Avoidance of Partially Ordered Patterns Research Directions and Open Problems Automata and Generating Trees History and Connections Tools from Graph Theory Automata Generating Trees The ECO Method Research Directions and Open Problems Asymptotics for Compositions History Tools from Probability Theory Tools from Complex Analysis Asymptotics for Compositions Asymptotics for Carlitz Compositions A Word on the Asymptotics for Words Research Directions and Open Problems Appendix A: Useful Identities and Generating Functions Appendix B: Linear Algebra and Algebra Review Appendix C: Chebychev Polynomials of the Second Kind Appendix D: Probability Theory Appendix E: Complex Analysis Review Appendix F: Using Mathematica and Maple Appendix G: C++ and Maple Programs Appendix H: Notation References Exercises appear at the end of each chapter.