The subject matter of this book might be labelled fairly accurately Intrinsic geometry of uniform spaces. {For an impatient reader, this means elements B5%), dimension theory D0%), function spaces A2^%), and special topics in topology.} As the term "geometry" suggests,We shall not be concerned with applications to functional analysis and topological algebra. However, applications to topology and specializations to metric spaces are of central concern; in fact, these are the two pillars on which the general theory stands. This dictum brings up a second exclusion: the book is not much concerned with restatements of the basic definitions or generalizations of the fundamental concepts. These exclusions are matters of principle. A third exclusion is dictated mainly by the ignorance of the author, excused perhaps by the poverty of the literature, and at any rate violated in several places in the book: this is extrinsic (combinatorial and differential) geometry or topology.