Here is the course announcement with a brief syllabus description.

An important organizational point not mentioned there: the grader for the class is Dmitry (Mitya) Kubrak, dmkubrak@MIT.EDU. If you are submitting your homework by email please send it to him (cc the instructor at bezrukav@math.mit.edu). The grader doesn't have scheduled office hours but feel free to meet him and discuss any questions you may have about homework grading.

Lecture notes by Mike Artin and by Pavel Etingof provide supplementary reading for the class.

Azumaya algebras and Amitsur cohomology are explained in some depth in handwritten notes by Vladimir Hinich.

Here are the scanned handwritten notes for Lecture 19 and Lecture 20 by Pavel Etingof.

The first homework is due on Thursday, 9/20.

The second homework is due on Thursday, 10/4.

The third homework is due on Thursday, 10/18.

Homework 4 is due on Thursday, 11/1.

Homework 5 is due on Monday, 11/19.

The last homework 6 is due on Monday, 12/10.

The list of suggested topics for the optional expository paper is here. The paper is due by December 12 (the end of the semester).