Here is the link to my personal course notes for this class. Notes (They might contain typos or logical errors.) They are created based on Ross's, Rudin's textbooks and Professor Zhou's lectures.

1. What's the difference between uniform continuity and continuity?
2. What's the difference between pointwise convergence and uniform convergence?
3. Is a series of continuous functions necessarily continuous?

• No, consider $f_n(x)=x^{n}-x^{n-1}$ and $\sum_n f_n(x)$ is not continuous.