Applied Mathematical Sciences 127. New York, NY: Springer (ISBN 0-387-25364-5/hbk). xiii, 344 p. EUR 69.95/net; sFr. 123.50; £ 54.00; $ 79.95 (2006).

The first edition of this excellent book appeared in 1998 (see

Zbl 0908.35134) see and became a standard reference for everyone interested in analysis and numerics of inverse problems in partial differential equations. The topic is of substantial and growing interest for mathematicians, physicists and engineers, and to graduate students in these areas as well. The book consists of the following Chapters: 1) Inverse problems, 2) Ill-posed problems and regularization, 3) Uniqueness and stability in the Cauchy problem, 4) Elliptic equations: single boundary measurements, 5) Elliptic equations: many boundary measurements, 6) Scattering problems, 7) Integral geometry and tomography, 8) Hyperbolic equations, 9) Inverse parabolic problems, 10) Some numerical methods. The second edition is considerably expanded and reflects important recent developments in the field, including new uniqueness and stability results for basic inverse problems, emerging financial applications, and new efficient reconstruction algorithms. Some of the research problems from the first edition have been solved, while most of them still await solutions.