Parameterized complexity studies a generalization of the notion of polynomial time where, in addition to the overall input size n, one also considers the effects on computational complexity of a secondary measurement, the parameter. The central notion of the field is fixed-parameter tractability (FPT), which refers to solvability in time f(k)nc, where f is some function (usually exponential) of the parameter k, and c is a constant. The subject unfolds in two basic complementary projects and associated mathematical toolkits: (1) How to design (and improve) FPT algorithms, for parameterized problems that admit them and (2) How to gather evidence that a parameterized problem probably does not admit an FPT algorithm.