Profinite groups are of interest to mathematicians working in a variety of areas, including number theory, abstract groups, and analysis. The underlying theory reflects these diverse influences, with methods drawn from both algebra and topology and with fascinating connections to field theory. This is the first book to be dedicated solely to the study of general profinite groups. It provides a thorough introduction to the subject, designed not only to convey the basic facts but also to enable readers to enhance their skills in manipulating profinite groups. The first few chapters lay the foundations and explain the role of profinite groups in number theory. Later chapters explore various aspects 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.

It was 1905 when the man destined to become Waco's photographer first opened his shop.Fred Gildersleeve documented the city he loved, establishing his legacy through iconic images that have become Waco's visual memory. The 186 Gildersleeve images within capture the spirit of early Waco. Born in 1880 in Boulder, Colorado, Gildersleeve spent most of his childhood in Kirksville, Missouri. Throughout his early years, Gildersleeve sold his pictures for 25 cents apiece to pay for his education, working his way through photography school in Effingham, Illinois before launching his career in Waco. An adventurer, Gildersleeve was known for speeding through town on an Excelsior motorbikeaand later in a Model T Fordawith his assistant in the sidecar. He avidly took pictures of everyday life in Waco, becoming the official photographer for Baylor and the State Fair of Texas. From special occasions to sporting events, from construction projects to key figures, Gildersleeve documented Waco's growth as a thriving industrial city during the early days of the twentieth century. Gildersleeve's photos are not just history; they are art. He pioneered panoramas and aerial shots using Waco as his subject. Gildersleeve's photos are now known for their clarity and detail that resemble and surpass modern-day digital photography. The photos in this book take viewers back in time to their favorite Waco landmarks and do so with timeless creativity.