Written at a level accessible to first-year graduate students, this book covers five major topics in numerical analysis: fast multipole methods, eigenvalue problems for differential equations, hierarchic modeling in mechanics, wavelets from filter banks, and multilevel methods. The authors are renowned experts and provide up-to-date overviews, complete with extensive bibliographies, along with new and previously unpublished material. Both students and experienced researchers will find this volume an ideal starting point for pursuing these important topics or applying the methods to their own research. The book contains proceedings from the seventh EPSRC Numerical Analysis Summer School, held in 1996.