Abstract
Activities are certain statistics associated to spanning forests and more general objects which can be used for defining the Tutte polynomial. This chapter is intended to serve as an introduction to activities for graphs and matroids. We describe various activity expansions of the Tutte polynomial. Tutte's original spanning forest activities. Gordon and Traldi's subgraph activities. Gessel and Sagan's depth-first search activities. Bernardi's embedding activities. Gordon and McMahon's generalized subgraph activities. Las Vergnas' orientation activities. Etienne and Las Vergnas' activity bipartition. Crapo's activity interval decomposition. Las Vergnas' active orders. Shellability and the algebraic combinatorics of activities.
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