The preliminary syllabus for this course is:
Atiyah, M. F. & Macdonald, I. G. Introduction to Commutative Algebra.
Chapter 1 (all)
Chapter 2 (all)
Chapter 3 (all)
Chapter 4 (all)
From Chapter 5: p.59-61, ending at the heading "Going up theorem". Also Prop. 5.12 and Prop. 5.13.
Chapter 6 (all)
Chapter 7 (all)
Chapter 8 (all)
From Chapter 9: p. 93-95, ending at the heading "Dedekind domains".
From Chapter 11: p. 116-122, up to and including Cor. 11.18.
The plan is to also refer to Geir Ellingsrud's Commutative Algebra, available here, for exercises and some of the material covered.