A systematic presentation of the basics of the theory of linear abstract functional differential equation . is given. This theory allows us to consider from a single point of view numerous classes of equations. previously studied in relation to each other, Specifically , Equations with singularities , with impulse effects , Integro-differential , with a declining argument, some perturbations of the Poisson equation... Theorems of general theory open up new possibilities for a computational experiment in the study of boundary problems, control problems and minimization of quadratic functionality in various spaces. A separate chapter is devoted to nonlinear equations and boundary problems, as well as the problem of minimizing nonlinear functions. For researchers, teachers, graduate students and students of mathematical faculties, whose interests are related to differential and functional-differential equations