The curriculum will consist of parts of the following two books:
J. N. McDonald and N. A. Weiss, A course in real analysis, 2nd edition, Academic Press, from chapters 14.4 to 14.6 (cover essentially the same as 2.4 and 2.5 in Analysis Now, but has more exercises).
G. K. Pedersen, Analysis Now, 1989. Springer. ISBN: 978-0-387-96788-2. Corrected 2nd printing. From chapters 2.4 and 2.5, 3.2 to 3.4, 4.1 to 4.6, 5.1. Link to Springer's homepage for this book.