Information geometry, which began as an investigation of the natural differential geometric structure possessed by families of probability distributions, is offered here in a complete treatment, translated from the original 1993 work in Japanese. The topic is applicable to information theory, stochastic processes, and systems, including neurocomputing. The authors, who assume some knowledge of statistics, systems theory and information theory, begin with an introduction to differential geometry and the theory of dual connections, before describing statistical inference, geometry of time series and linear systems, multiterminal information theory and statistical inference, information geometry for quantum systems, concluding with a grab-bag of applications including geometry of convex analysis, linear programming and gradient flows, neuro-manifolds and nonlinear systems, lie groups and transformation models.