The course gives an up-to-date and modern overview of the main concepts in Functional Analysis. Functional analytic properties and several examples of Banach and Hilbert spaces arising in several branches of mathematics are studied to show how functional analysis is a unifying theme in different mathematical fields.

Functional analysis is mainly concerned with the study of vector spaces and operators acting upon them. It provides powerful tools in handling several problems in applied mathematics and theoretical physics. It is also basic for the understanding and development of very many other mathematical theories like the Theory of Partial Differential Equations and the Theory of Operators.