This voluminous book is intended as an elementary introduction aimed at undergraduate university students. Each section states (without proof) relevant theorems and then proceeds by means of simple examples and exercises. An important feature is that the exposition is richly accompanied by computer algebra code (equally distributed between Matlab, Mathematica and Maple). The major part of the book is devoted to classical linear theory (both for systems and higher order equations). The necessary material from linear algebra is also covered. More advanced topics include numerical methods (Euler, Runge-Kutta), stability of equilibria, bifurcations, Laplace transforms and the power series method. The elementary character of the book makes it accessible to a wide audience of students; it also serves as a simple introduction to the above mentioned computer programs.