My lectures are largely based on the lecture notes (in French) by Bernard Maurey:

https://webusers.imj-prg.fr/~bernard.maurey/ths012.html

Here are some classical textbooks (only the first chapters are relevant for this class):

Brezis, Haim

Functional analysis, Sobolev spaces and partial differential equations.

Universitext. Springer, New York, 2011. xiv+599 pp 

Rudin, W.: Functional Analysis, McGraw-Hill Science, 1991

Yosida, Kōsaku

Functional analysis.

Reprint of the sixth (1980) edition. Classics in Mathematics. Springer-Verlag, Berlin, 1995. xii+501 pp