The chapter introduces the basic concepts of Markov chains, including the definition of a Markov process and chain, examples, and the connection with matrix theory. It covers the classification of states and chains, and provides a brief summary of prerequisites. The chapter also discusses absorbing and regular Markov chains, fundamental matrices, and their applications in various fields such as random walks, sports, genetics, and learning theory. The authors emphasize the practical aspects of the theory, such as the ease of programming matrix operations for high-speed computers, and highlight the simplicity of the matrix expressions compared to those involving eigenvalues. The chapter concludes with a detailed table of contents and appendices that summarize basic notation, definitions, and formulas.The chapter introduces the basic concepts of Markov chains, including the definition of a Markov process and chain, examples, and the connection with matrix theory. It covers the classification of states and chains, and provides a brief summary of prerequisites. The chapter also discusses absorbing and regular Markov chains, fundamental matrices, and their applications in various fields such as random walks, sports, genetics, and learning theory. The authors emphasize the practical aspects of the theory, such as the ease of programming matrix operations for high-speed computers, and highlight the simplicity of the matrix expressions compared to those involving eigenvalues. The chapter concludes with a detailed table of contents and appendices that summarize basic notation, definitions, and formulas.