This is the softcover reprint of the English translation of 1971 (available from Springer since 1989) of the first 4 chapters of Bourbaki's Topologie générale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structures are introduced and applied to topological groups. Real numbers are constructed and their properties established. Part II, comprising the later chapters, Ch. 5-10, is also available in English in softcover. TOC:From the Contents: Open sets, Neighbourhoods, Closed Sets; Continuous Functions; Subspaces, Quotient Spaces; Product of Topological Spaces; Open mappings and closed mappings; Filters; Limits; Hausdorff Spaces and Regular spaces; Compact Spaces and Locally Compact Spaces; Proper mappings; Connectedness; Exercises; Uniform Structures; Topological Groups; Real Number; Exercises