This monograph presents the theoretical foundations of computational mathematics in Frechet spaces, which are the closest generalization of Banach spaces. A Frechet space is complete metrizable locally convex space (LCS). The monograph presents a unified approach to studying of computational processes in Banach and Frechet spaces: the study of computational processes considered in Frechet space is based on the study of computational processes in Banach spaces. Vice versa, for the study of computational processes in Banach spaces, we use the theory of Frechet spaces. In particular, attempts at a unified approach are presented in the study of the theories of best approximation, projective processes, spline algorithms, and homomorphisms, when the case of Banach spaces is part of the general approach. Many topological linear spaces of continuous, differentiable or holomorphic functions which arise in connection with various problems in analysis and its applications require a countable number of deviation measurements with respect to seminorms, which produce Frechet spaces. Therefore, it is a rapidly developing part of functional analysis and has the important applications in mathematical physics and quantum mechanics...

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