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Professor Bennett's work explores the potential for inverse theory, emphasizing possibilities rather than expedient or rudimentary applications. In addition to interpolating the data and adding realism to the model solutions, the methods can yield estimates for unobserved flow variables, forcing fields, and model parameters. Inverse formulations can resolve ill-posed modeling problems, lead to design criteria for oceanic observing systems, and enable the testing of models as scientific hypothesis. Ocean models considered range from linear, finite-dimensional systems of equality and inequality constraints, to nonlinear, regional primitive-equation models. Examples from the recent oceanographic literature are analyzed, and several outstanding research problems are surveyed. The methods employ solution techniques including Kalman filters and smoothers, representer expansions and descent algorithms. Exercises of varying difficulty rehearse technical skills and supplement the central theoretical development.