There is no single book.
love of mathematics
We will closely follow Lovasz's well known book of Combinatorial Problems and Exercises. I will also show several applications of combinatorics in other fields of mathematics, computer science and statistical physics, using different sources.
Some algebra (especially linear algebra), some discrete probability, and mathematical maturity.
This will be a basic introduction to combinatorics at the graduate level.
We will cover topics such as enumeration, symmetry, partial orders, set systems, Ramsey theory, discrepancy, additive combinatorics and quasirandomness. There will be emphasis on general techniques, including probabilistic methods, linear-algebra methods, analytic methods, topological methods and geometric methods.