Order dependencies (ODs) describe a relationship of order between lists of attributes in a relational table. ODs can help to understand the semantics of datasets and the applications producing them. They have applications in the field of query optimization by suggesting query rewrites. Also, the existence of an OD in a table can provide hints on which integrity constraints are valid for the domain of the data at hand. This work is the first to describe the discovery problem for order dependencies in a principled manner by characterizing the search space, developing and proving pruning rules, and presenting the algorithm Order, which finds all order dependencies in a given table. Order traverses the lattice of permutations of attributes in a level-wise bottom-up manner. In a comprehensive evaluation, we show that it is efficient even for various large datasets.