  We discuss a notion of shuffle for trees which extends the usual notion of a
shuffle for two natural numbers. We give several equivalent descriptions, and
prove some algebraic and combinatorial properties. In addition, we characterize
shuffles in terms of open sets in a topological space associated to a pair of
trees. Our notion of shuffle is motivated by the theory of operads and occurs
in the theory of dendroidal sets, but our presentation is independent and
entirely self-contained.
