This book is somewhat similar to another wonderful book by Springer-Verlag: "Proof from the Book" by Aigner and Ziegler. Both books illustrate the sheer beauty of selected theorems and proof techniques rather than develop systematically a discipline. As a result, reading is an adventure rather than a task. The pace is brisk, the writing style is direct. The reader is left with the impression that there is much research to do, and that mathematics is not cast in stone or heavy handbooks, but is a growing body of knowledge. Therefore, I would suggest this book to any beginning researcher in Computer Science, Mathematics, or Operation Research.
There are 26 lectures, covering well-known topics as well as rather obscure ones. To give the reader a flavor of the book here are some:
PAC-learning and Occam's razor;
Kolmogorov complexity, the universal distribution, and worst-case vs. average-case;
Hilbert's 10th problem;
P=NP with probability;
The Berman-Hartmanis conjecture;
Lower bounds for the parity function;
Quantum search algorithms.
The book is suitable for advanced undergraduates and beginning graduate students. Overall, this book proves once again that Springer-Verlag is among the best publishers in the mathematical sciences, and is definitely the most innovative in mathematical education.