  We study an abstract notion of tree structure which lies at the common core
of various tree-like discrete structures commonly used in combinatorics: trees
in graphs, order trees, nested subsets of a set, tree-decompositions of graphs
and matroids etc.
  Unlike graph-theoretical or order trees, these _tree sets_ can provide a
suitable formalization of tree structure also for infinite graphs, matroids,
and set partitions. Order trees reappear as oriented tree sets.
  We show how each of the above structures defines a tree set, and which
additional information, if any, is needed to reconstruct it from this tree set.
