This book is an interpolation between a monograph and a handbook. It is aimed at readers who want to familiarize themselves with the fundamental mathematical ideas and techniques of wavelets while also gaining an overview of how the theory is currently applied. The book is intended for readers with knowledge from higher years of study: familiarity with applications of linear algebra, Fourier series, and Fourier integrals is assumed. However, additional knowledge is desirable for a better understanding of the theory. An overly excessive mathematical precision would place too high demands on the readers this book targets. The solution to this dilemma is a compromise: the authors forgo some mathematical details and instead refer to further representations.