These will be introductory lectures surveying GW, MNOP and GV invariants - all different ways of counting curves. For a string theorist this involves seeing the curve as, respectively, the world sheet of a string, a D-brane, or a BPS thingummy. I will describe a 4th way via stable pairs, which in effect means counting D-branes (or stable objects of the derived category, to mathematicians) after a change of stability condition.