This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book introduces the notion of random variables, random sequences, and stochastic processes. It considers the foundation for determining minimum mean-square error filters. The most common adaptive filters, which are used during the adaptation process, are the finite impulse response filters types. These are preferable because they are stable, and no special adjustments are needed for their implementation. The book presents the theory and properties of the eigenvalues and the properties of the error surface. It provides the most celebrated algorithm of adaptive filtering, the least-mean-square algorithm (LMS) algorithm. The LMS algorithm approximates the method of steepest descent. The book presents a number of variants of the LMS algorithm, which have been developed since the introduction of the LMS algorithm. It describes the least squares and recursive least squares signal processing.