Chapter 2 of Munkres; everything but section 21; in section 19, we only considered finite products.
Chapter 3 of Munkres; sections 23, 24, 26, 27. We did not cover uniform continuity or the Lebesgue number lemma.
Chapter 9 of Munkres. We covered sections 51, 52, 55, some of 58, 59.
Chapter 11 of Munkres. We covered sections 68, 69, 70, 71.
Chapter 12 of Munkres. Sections 74 and 75.
The only proof that I would consider "too hard" for the exam is Theorem 27.1, which says that closed intervals of the real line are compact.