Material for the course on Algebraic D-modules (fall 2008).
The course meets Monday, Wednesday 9:30--11 at 2-135.

Course announcement.

Homework 1, due 9/24.
Homework 2, due 10/15.
Homework 3, due 10/29.
Homework 4, due 11/17.
Homework 5.

Some references:
The book by A. Borel "Algebraic D-modules" contains much of what will be covered in the first half of the course.
The book by Kashiwara "D-modules and microlocal calculus" emphasizes the role of b-functions.
Malgrange's Bourbaki talk from 1977/78 (LNM 710) gives a nice explanation of microlocalization and involutivity of the singular support.
Bersntein's notes is a very good, albeit concise, exposition of the key results including application to Kazhdan-Lusztig conjectures.
A course by J.-P.Schneiders explains some of the basic constructions.
A recent book "D-modules, perverse sheaves and representation theory" by Hotta, Takeuchi and Kashiwara touches upon most of the topics of the course.

!-crystals are discussed in section 7 (pp 284--298) of the unfinished book "Quantization of Hitchin's integrable system and Hecke eigensheaves" by Beilinson and Drinfeld available at their seminar page. (References as of October 2008).
Ben-Zvi's page contains further links. By the way, his paper with Nevins (JAMS 17 (2004) 155-179) shows that various definitions of D-modules agree sometimes even for singular varieties.
In the discussion of Kazhdan-Lusztig conjectures I followed MacPherson's argument described in the Bourbaki talk Quelques applications de la cohomologie d'intersection by T. Springer. See also Soergel's ICM (1994) talk "Gradings on representation categories" for a discussion of grading on categories and its relation to Kazhdan-Lusztig conjectures.
The definition of unipotent nearby cycles was introduced in Beilinson's paper who to glue perverse sheaves, a typed version can be found here.
A discussion of b-functions and multiplier ideals appears in recent papers of Budur and Budur, Saito.