The Burrows-Wheeler Transform is a text transformation scheme that has found applications in different aspects of the data explosion problem, from data compression to index structures and search. The BWT belongs to a new class of compression algorithms, distinguished by its ability to perform compression by sorted contexts. More recently, the BWT has also found various applications in addition to text data compression, such as in lossless and lossy image compression, tree-source identification, bioinformatics, machine translation, shape matching, and test data compression. This book will serve as a reference for seasoned professionals and researchers in the area, while providing a gentle introduction that makes it accessible for senior undergraduate students or first-year graduate students embarking upon research in compression, pattern matching, full text retrieval, compressed index structures, or other areas related to the BWT.