An accessible and concrete introduction to the main principles of ordinary differential equations. The study of differential equations is approached from a dynamical systems perspective, so there is an emphasis on qualitative questions and the evolution of solutions. Important principles are sectioned off to present a coherent picture of the study of differential equations, and the questions driving the theory are discussed.Principles of Differential Equations: Exposes the roots of modern dynamical systems in order to help readers gain a solid foundation of ordinary differential equations. Sticks strictly to core ideas and firmly adheres to the principle that any result that is part of the core is worth carefully developing and proving. Provides an excellent foundation for most of the sub-disciplines of differential equations and dynamical systems.