This is the first book to be dedicated entirely to profinite groups, an area of algebra with important links to number theory and other areas of mathematics. It provides a comprehensive overview of the subject; prerequisite knowledge is kept to a minimum, and several major theorems arepresented in an accessible form. The book would provide a valuable introduction for postgraduate students, or form a useful reference for researchers in other areas. The first few chapters lay the foundations and explain the role of profinite groups in number theory. Later chapters explore variousaspects of profinite groups in more detail; these contain accessible and lucid accounts of many major theorems. Prerequisites are kept to a minimum with the basic topological theory summarized in an introductory chapter.