This text introduces elementary ordinary differential equations in a clear and concise fashion. Designed around a single-semester undergraduate course, Ordinary Differential Equations explores key concepts along with various real-world applications. In particular, we discuss common techniques for solving first-order differential equations, basic numerical methods, second-order homogeneous and nonhomogeneous differential equations, the generalization to higher-order linear differential equations, the Laplace transform method, linear systems of differential equations, and nonlinear systems of differential equations.