“Functional analysis is concerned with the study of functions and function spaces, combining techniques borrowed from classical analysis with algebraic techniques. Modern functional analysis developed around the problem of solving equations with solutions given by functions. After the differential and partial differential equations, which were studied in the eighteenth century, came the integral equations and other types of functional equations investigated in the nineteenth century, at the end of which arose the need to develop a new analysis, with functions of an infinite number of variables instead of the usual functions.” Paycha, S. (2006). Introductory article: Functional analysis. In Encyclopedia of Mathematical Physics (pp. 88–96). Academic Press.
Books on analysis can be found in the Mathemathics Library Stacks shelved under call number range 515 to 516.