  We introduce the concept of a dendroidal set. This is a generalization of the
notion of a simplicial set, specially suited to the study of operads in the
context of homotopy theory. We define a category of trees, which extends the
category $\Delta$ used in simplicial sets, whose presheaf category is the
category of dendroidal sets. We show that there is a closed monoidal structure
on dendroidal sets which is closely related to the Boardman-Vogt tensor product
of operads. Furthermore we show that each operad in a suitable model category
has a coherent homotopy nerve which is a dendroidal set, extending another
construction of Boardman and Vogt. There is also a notion of an inner Kan
dendroidal set which is closely related to simplicial Kan complexes. Finally,
we briefly indicate the theory of dendroidal objects and outline several of the
applications and further theory of dendroidal sets.
