<P>A <I>CHOICE</I> "Outstanding Academic Title," the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, <I>Combinatorics of Permutations</I>, third edition continues to clearly show the usefulness of this subject for both students and researchers.</P><P>The research in combinatorics of permutations has advanced rapidly since this book was published in a first edition. Now the third edition offers not only updated results, it remains the leading textbook for a course on the topic.</P><P>Coverage is mostly enumerative, but there are algebraic, analytic, and topological parts as well, and applications.</P><P>Since the publication of the second edition, there is tremendous progress in pattern avoidance (Chapters 4 and 5). There is also significant progress in the analytic combinatorics of permutations, which will be incorporated. </P><P>¿A completely new technique from extremal