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Since the injective envelope and the projective cover were defined by Eckmann and Bas in the 1960s, they have had an influence on the development of homological algebra, ring theory and module theory. In the 1980s Enochs introduced the flat cover and conjectured that every model has such a cover over every ring. This volume provides the uniform methods and systematic treatment to study general envelopes of flat cover. It shows that Enoch's conjecture is true for a large variety of rings, and then presents the applications of the results. It is suitable as a reference book and textbook for researchers and graduate students who have an interest in the field.