The present book is intended to be a systematic text on topological vector spaces and presupposes familiarity with the elements of general topology and linear algebra. The author has found it unnecessary to rederive these results, since they are equally basic for many other areas of mathematics, and every beginning graduate student is likely to have made their acquaintance. Simi- larly, the elementary facts on Hilbert and Banach spaces are widely known and are not discussed in detail in this book, which is: plainly addressed to those readers who have attained and wish to get beyond the...