Companion Lecture Notes to Atiyah-MacDonald? Is there a set of lecture notes that follow Atiyah-MacDonald and expand on the dense passages, point out typos and so forth?
 A: Here are two links where you can find further links to downloads such as you are looking for:
http://math.berkeley.edu/~aboocher/research.html
http://people.brandeis.edu/~igusa/Courses.html
I myself was/am in the market for these. In passing I saw a mention of this book:
http://www.amazon.com/Commutative-Algebra-Mathematical-Society-Student/dp/0521646235
I have not looked at it, but it might be useful. The author is actually acknowledged in the preface to "A&M."
A: (Sorry, this post should really be a comment to the answer by Oliver E. Anderson, but I don't have enough reputation to be able to comment yet. Please someone re-post it as a comment instead of me. If you notify me, I'll delete this answer.)
The latest revision of the textbook by Altman and Kleiman can be found at this MO answer. Be sure to get at least the 2017 version or newer, which was a substantial expansion.
A: You can try the following A. Altman and S. Kleiman: A term of commutative algebra, 2012. 
You can read it for free here:
http://web.mit.edu/18.705/www/12Nts.pdf
