The twin themes of computational complexity and information pervade this book. It starts with an introduction to information-based complexity, that is, the computational complexity of continuous mathematical models. It then moves to a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, value of information in computation, assigning values to mathematical hypotheses, and mathematical finance. The style is informal, and the goal is motivation and insight. Precise statements and proofs can be found in the...