From the reviews of the first edition: This book contains detailed lecture notes on five topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. Current (unsolved) problems are also described and directions for future research are given. The book is suitable for first year graduate students in applied mathematics and for professional mathematicians. (L'Enseignement Mathematique, Vol. 48 (1-2), 2002)