- What is geometric combinatorics?-An overview of the graduate summer school
- Bibliography

*A. Barvinok, Lattice points, polyhedra, and complexity*

- Introduction
- Inspirational examples. Valuations
- Identities in the algebra of polyhedra
- Generating functions and cones. Continued fractions
- Rational polyhedra and rational functions
- Computing generating functions fast
- Bibliography

*S. Fomin and N. Reading, Root systems and generalized associahedra*

- Introduction
- Reflections and roots
- Dynkin diagrams and Coxeter groups
- Associahedra and mutations
- Cluster algebras
- Enumerative problems
- Bibliography

*R. Forman, Topics in combinatorial differential topology and geometry*

- Introduction
- Discrete Morse theory
- Discrete Morse theory, continued
- Discrete Morse theory and evasiveness
- The Charney-Davis conjectures
- From analysis to combinatorics
- Bibliography

*M. Haiman and A. Woo, Geometry of $q$ and $q,t$-analogs in combinatorial enumeration*

- Introduction
- Kostka numbers and $q$-analogs
- Catalan numbers, trees, Lagrange inversion, and their $q$-analogs
- Macdonald polynomials
- Connecting Macdonald polynomials and $q$-Lagrange inversion; $(q,t)$-analogs
- Positivity and combinatorics?
- Bibliography

*D. N. Kozlov, Chromatic numbers, morphism complexes, and Stiefel-Whitney characteristic classes*

- Preamble
- Introduction
- The functor Hom$(-,-)$
- Stiefel-Whitney classes and first applications
- The spectral sequence approach
- The proof of the Lovász conjecture
- Summary and outlook
- Bibliography

*R. MacPherson, Equivariant invariants and linear geometry*

- Introduction
- Equivariant homology and intersection homology (Geometry of pseudomanifolds)
- Moment graphs (Geometry of orbits)
- The cohomology of a linear graph (Polynomial and linear geometry)
- Computing intersection homology (Polynomial and linear geometry II)
- Cohomology as functions on a variety (Geometry of subspace arrangements)
- Bibliography

*R. P. Stanley, An introduction to hyperplane arrangements*

- Basic definitions, the intersection poset and the characteristic polynomial
- Properties of the intersection poset and graphical arrangements
- Matroids and geometric lattices
- Broken circuits, modular elements, and supersolvability
- Finite fields
- Separating hyperplanes
- Bibliography

*M. L. Wachs, Poset topology: Tools and applications*

- Introduction
- Basic definitions, results, and examples
- Group actions on posets
- Shellability and edge labelings
- Recursive techniques
- Poset operations and maps
- Bibliography

*G. M. Ziegler, Convex polytopes: Extremal constructions and $f$-vector shapes*

- Introduction
- Constructing 3-dimensional polytopes
- Shapes of $f$-vectors
- 2-simple 2-simplicial 4-polytopes
- $f$-vectors of 4-polytopes
- Projected products of polygons
- A short introduction to polymake
- Bibliography