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The Maximum Entropy Method and the related Bayesian Probability Theory have recently become somewhat better known to research workers; but the power of these methods to resolve the true structures underlying many kinds of data is still not as widely recognized as it ought to be. This book is the first readily available account of such methods. It grew out of a series of interdisciplinary seminars, organized by the editors, and given by leading proponents of maximum entropy techniques in the UK. The written versions are intended to introduce the reader to the principles of probability theory, viewed as the logic of inference, and to explain the role that entropy plays in the assignment of probabilities. The chapters concerned with applications show how the resulting algorithms can be implemented and how they work out in practice. In addition, new light is shed upon the relation between statistical and dynamical theories in physics, and on the confusion which surrounds the Second Law of Thermodynamics.