We will discuss here the topology of pointwise convergence on function spaces. During the last decades these function spaces have played a prominent role in both general and infinite-dimensional topology. Arhangelski  initiated the systematic study of them.
Methods and techniques from general topology, functional analysis, infinite-dimensional topology and descriptive set theory primarily are used for the study of these function spaces. This mix of methods and techniques from several disciplines makes the subject particularly interesting. Several monographs, surveys and research papers were written containing many interesting and diverse results, see e.g., Arhangelski [2,3,4], McCoy and Ntantu , Baars and de Groot , van Mill , Cauty , Dobrowolski, Marciszewski and Mogilski , Cauty, Dobrowolski and Marciszewski  and Marciszewski .