This second edition is the successor to "Direct methods in the calculus
of variations" which was published in the Applied Mathematical Sciences
series and is currently out of print. Although the core and the
structure of the present book is similar to the first edition, it is
much more than a revised version. Fifteen years have passed since the
publication of the "Direct methods in the calculus of variations" book
and since the subject is a very active one, almost half of the book
presently consists of new material. The perspective has also slightly
changed, indeed, a new subject, "quasiconvex analysis" has now been
developed. The present edition, which is essentially a reference book on
the subject of quasiconvex analysis can be used, as was the earlier
book, for an advanced course on the calculus of variations.