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This is 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; and provides an excellent foundation for most of the sub disciplines of differential equations and dynamical systems.