Suitable for both postgraduate students and researchers in the field of operator theory, this book is an excellent resource providing the complete proof of the Brown-Douglas-Fillmore theorem.The book starts with a rapid introduction to the standard preparatory material in basic operator theory taught at the first year graduate level course.To quickly get to the main points of the proof of the theorem, several topics that aid in the understanding of the proof are included in the appendices.These topics serve the purpose of providing familiarity with a large variety of tools used in the proof and adds to the flexibility of reading them independently.