- Fundamental theorems. Matching structure.
- Hall's theorem. Tutte's matching theorem. (Notes for Lecture 1)
- The matching polytope. (Notes for Lecture 2)
- Tight cuts, bricks and braces. (Notes for Lecture 3)

- Pfaffian orientations.
- Kasteleyn's theorem. Drawing Pfaffian graphs with crossings. (Notes for Lecture 4)
- Drawing Pfaffian graphs with crossings. Pfaffian orientations of bipartite graphs. (Notes for Lecture 5)

- Matchings in regular graphs.
- (Notes for Lecture 6)
- Exponentially many perfect matchings in bipartite graphs: Voorhoeve's theorem. Gurvits's proof of van der Waerden's conjecture and Schrijver's theorem. (Monique Laurent and Alexander Schrijver ``On Leonid Gurvits's proof for permanents". Available on Alexander Schrijver's homepage.)
- Exponentially many perfect matchings in cubic graphs. (Esperet, Kardos, King, Kral and N. ``Exponentially many perfect matchings in cubic graph". Paper and slides.)