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The present book speaks about the topological ring of Colombeau's full generalized numbers, the space of Colombeau's full generalized functions and an aplications. We generalize a result of existence and uniqueness of solution for a boundary-initial value problem of the parabolic type which has been studied by Colombeau and Langlais, 1990. For this, we apply the topological results such as density and completude already explicited in the same chapter of the problem.