I am teaching this course jointly with Yongqi Feng.
In the 1st half I discuss higher dim (comm alg from alg geom);
in the 2nd half Yongqi discuss dim=1 (comm alg from alg num thy).
We hope this arrangement makes sense.
Atiyah and Macdonald - Introduction to Commutative Algebra
Eisenbud - Commutative Algebra with a View towards Algebraic Geometry
Liu - Algebraic Geometry and Arithmetic Curves
Marcus - Number Fields
Matsumura - Commutative Ring Theory
Stevenhagen - online lecture notes