These notes introduce the central concepts surrounding wavelets and their applications. By focusing on the essential ideas and arguments, the authors enable readers to get to the heart of the matter as quickly as possible. A list of references guides readers interested in further study to the appropriate places in the literature for detailed proofs and real applications. The authors begin with the notion of time-frequency analysis, present the multiresolution analysis and basic wavelet construction, introduce the many friends, relatives, and mutations of wavelets, and finally give a selection of applications. This book is suitable for beginning graduate students and above. A preliminary chapter containing some of the prerequisite concepts and definitions is included for reference.