Besides a general renovation, the text has improved the topics related to the Hahn-Banach theorem . there is a whole new chapter on vector-valued Hahn-Banach theorems and an enlarged presentation of the Banach-Stone theorems. The text remains a nice expository book on the fundamentals of the theory of topological vector spaces. --Luis Manuel Sanchez Ruiz, Mathematical Reviews, Issue 2012a This is a nicely written, easy-to-read expository book of the classical theory of topological vector spaces. The proofs are complete and very detailed. The comprehensive exposition and the quantity and variety of exercises make the book really useful for beginners and make the material more easily accessible than the excellent classical monographs by Köthe or Schaefer. this is a well-written book, with comprehensive proofs, many exercises and informative new sections of historical character, that presents in an accessible way the classical theory of locally convex topological vector spaces and that can be useful especially for beginners interested in this topic. --José Bonet, Zentralblatt MATH 1219 Praise for the First Edition: This is a very carefully written introduction to topological vector spaces.

But it is more. The enthusiasm of the authors for their subject, their untiring efforts to motivate and explain the ideas and proofs, and the abundance of well-chosen exercises make the book an initiation into a fascinating new world. The reader will feel that he does not get only one aspect of this field but that he really gets the whole picture. --Gottfried Köthe, Rendiconti del Circolo Matematico di Palermo, Series II, Volume 35, Number 3, September 1986.