This is the third in a series of three courses on discrete geometry. This advanced course will cover a selection of the following topics (depending on the interests of the audience):

1. Oriented Matroids along the lines of the book Oriented Matroids by Björner, Las Vergnas, Sturmfels, White, and Ziegler; and/or

2. Triangulations along the lines of the book Triangulations by de Loera, Rambau, and Santos; and/or

3. Discriminants and tropical geometry along the lines of the book Discriminants, Resultants, and multidimensional determinants by Gelfand, Kapranov, and Zelevinsky; and/or

4. Combinatorics and commutative algebra along the lines of the book Combinatorics and commutative algebra by Stanley.