This introductory courses on (Ordinary) Differential Equations are mainly for the people, who need differential equations mostly for the practical use in their own fields. So we try to provide basic terminologies, concepts, and methods of solving various types of differential equations as well as a rudimentary but indispensable knowledge of the underlying theory and some related applications. The prerequisites of the courses is one- or two- semester calculus course and some exposure to the elementary theory of matrices like determinants, Cramerâ€™s Rule for solving linear systems of equations, eigenvalues and eigenvectors. Table of Contents Differential Equations Part I Basic Theory Chapter 1 Introduction Chapter 2 First Order Differential Equations Chapter 3 Mathematical Modelling and Applications Chapter 4 Linear Second Order Equations Chapter 5 Applications of Second Order Equations Differential Equations Part II Series Solutions Chapter 1 Euler Equations Chapter 2 Series Solutions of Linear Equations Chapter 3 Special Functions: Bessel Functions and Legendre Polynomials Differential Equations Part III Systems of Differential Equations Chapter 1 Systems of Linear Equations Chapter 2 Stability of Autonomous Systems