The following are some courses that I have previously taught:

Spring 2018, Math 63CM, Modern mathematics: continuous methods Course webpage
Winter 2018, Math 205B, Real analysis (Functional analysis) Course webpage
Spring 2017, Math 63CM, Modern mathematics: continuous methods Course webpage
Autumn 2016, Math 175, Elementary functional analysis Course webpage
Autumn 2016, Math 256B, Topics in PDEs Course webpage
Cambridge Part II Linear analysis

I will follow quite closely the lecture notes of Mihalis Dafermos. (Supplementary notes on Theorem 8.2)

Example Sheet 1 Example Sheet 2 Example Sheet 3 Example Sheet 4

Cambridge Part III Introduction to nonlinear wave equations

Lecture notes Review on Fourier analysis Example Sheet 1 Example Sheet 2 Example Sheet 3