The focus of this seminar was partially ordered sets (posets), which appear all throughout mathematics. A partially ordered set is a set with an ordering (e.g., the set of natural numbers under divisibility; the set of integers under the usual ordering; the set of subsets of a set under set inclusion). The theory of posets was applied using a tool, known as Möbius inversion, to compute the famous Euler totient function from number theory. Posets were represented as graphs, and graph colorings were also discussed. Students learned about other concepts related to posets, such as the mysterious combinatorial reciprocity, lattice polytopes, and Catalan objects.