Here are the slides of the four-hour course D-finiteness: Algorithms and Applications, given at EJCIM'07:

1. Part 1: Definitions and Closure Properties, Bruno Salvy
2. Part 2: Fast Algorithms for Functions, Alin Bostan
3. Part 3: Algorithms for Sequences, Bruno Salvy
4. Part 4: Multivariate Case, Frédéric Chyzak

Our Lecture Notes (in French) are also available. The computer-aided treatment of Apéry's proof of irrationality of zeta(3) demonstrated in Part 1 is also available in extended form as a Maple session (second item in Volume III).