This chapter introduces functional calculus. As most economic models in which there is maximization of functionals over continua require a generalized form of calculus, the material in this chapter constitutes a fundamental stepping stone to distributional or intertemporal optimization. The characterization of the properties of functionals over varieties, over variations, over uncertain outcomes, or combinations between them, is addressed. This allows for finding the common elements, and the differences, between Dixit-Stiglitz aggregators, expected utility, intertemporal utility, social welfare, and entropy functionals, and their optimization, with or without side constraints.