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This chapter introduces the reader to the basic ideas underlying ordinary differential equations. Knowledge of the basic rules of differentiation and integration is assumed; however, one of the main objectives of the chapter is to convey to the biologist reader, in an intuitive way, the basic idea of infinitesimal change and differentiation. The second main aim of this chapter is to provide an introduction to ordinary differential equations. The emphasis of this chapter is on usability. By the end of the chapter the reader will be able to formulate basic, but practically useful, differential equations; have a grasp of some basic concepts, including stability and steady states; and will also have an understanding of some basic methods to solve them. Furthermore, the reader will be able to critically evaluate differential equation models she may encounter in the research literature. The more general theoretical introduction into this topic is accompanied by fully worked case studies, including a differential equation model of the spread of malaria and a stability analysis of Cherry and Adler’s bistable switch.