The first lecture will be a general introduction to counting problems in Calabi–Yau threefold geometry, illustrated throughout by several manifestations of a single function of two variables, the partition function attached to the Calabi–Yau threefold geometry often called the local projective line. I’ll explain the Gromov–Witten, Donaldson–Thomas, Pandharipande–Thomas and noncommutative Donaldson–Thomas points of view, all of which include very explicit though highly non-trivial combinatorics.