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The study of planetary or solar magnetic fields explains natural magnetism as a phenomenon of magnetohydrodynamics. The kinematic dynamo theory, especially the fast dynamo treated in this volume, is somewhat simpler but still it presents formidable analytical problems related to chaotic dynamics, for example. This remarkable book presents the status of the theory, including techniques of numerical simulations and modelling, along with a summary of results to date. The first three chapters introduce the problem and present examples of fast dynamo action in flows and maps. The remaining nine chapters deal with various analytical approaches and model systems. The book addresses astronomers and geophysicists, researchers and students alike.