Textbook
James Munkres: Topology (second edition)
Syllabus
Chapter 1: §1-7, 9.
Chapter 2: §12-13, 15-22.
Chapter 3: §23-29 (but the notion of "limit point compactness" can be ignored)
Chapter 4: §30-35.
Chapter 5: §37-38.
Chapter 7: §45.
Chapter 9: §51-55, 58-59.
Notes on sets, nets and totally disconnected spaces.