Abdi Tadesse (PhD)Tadesse Dereje2020-12-092023-11-042020-12-092023-11-042012-02-02http://etd.aau.edu.et/handle/123456789/23907So far, many things were said about differential equations without time delay, the so called ordinary differential equations or partial differential equations and their solutions. Different techniques have been used to show the existence and uniqueness of the solution of initial value problem of these equations. Since time delay occurs naturally in just about every interaction of the real world, here in this project report we treat some differential equations with time delay, the so called linear functional differential equations or linear differential difference equations in general and for these equations, a complete theory can be developed using very basic tools. The project serves as an introduction to the more general types of differential difference equations. It also is intended to bring out the roles of the characteristic equation and Laplace transform to determine the solution of linear differential difference equations and to emphasize some of the differences between retarded and neutral equations.enExponentialEstimatesRetarded FunctionalDifferential EquationsThesis