The history of FD approximations goes back even further than that of calculus. The classical definition of a derivative is an example of a very simple FD formula. Although many basic FD properties follow quite immediately from Taylor expansions, numerous additional perspectives have proven very helpful both for deriving a wide range of FD formulas, and for understanding their different features (such as their accuracy near boundaries vs. in domain interiors). This chapter focuses on FD approximations on equispaced grids in one dimension, generalizing quite directly to Cartesian grids in higher dimensions. Further generalizations to mesh-free node layouts in multiple dimensions are discussed in Chapter 5.