The main purpose of this work is to study and classify the systems of differential-algebraic equations. This study includes the following aspects (1) Describe special types of systems for differential-algebraic equations that can be transformed to systems of differential equations. (2) Give some real life applications in which their mathematical modelings are systems of non-linear differential-algebraic equations. (3) Devoted systems of differential-algebraic equations that can be written in Hessenberge form. (4) Modify Laplace transform method to solve special types of system of linear differential-algebraic equations. (5) Solve special types of systems of non-linear differentialalgebraic equations (without transforming them to systems of differential equations) numerically by using linear multistep methods, Range-Kutta methods. (6) Use Adomain decomposition method to solve systems of differential-algebraic equations that can be transformed to systems of differential equations. (7) Solve systems of delay differential-algebraic equations that can not be transformed to systems of delay differential equations numerically by using linear multistep methods and Runge-Kutta methods.