A basic course in the theory of counting and graph theory. Topics in enumerative combinatorics may include: generating functions, compositions, partitions, Fibonacci numbers, permutations, cycle structure of permutations, permutations statistics, Stirling numbers of the first and second kind, Bell numbers, or inclusion-exclusion. Topics in graph theory may include: Eulerian and Hamiltonian cycles, matrix tree theorem, planar graphs and the 4-color theorem, chromatic polynomial, Hall's marriage theorem, stable marriage theorem, Ramsey theory, or electrical networks.