In Section 18.2 we introduced the space of conormal distributions associated with a submanifold Y of a manifold X. This is a natural extension of the classical notion of multiple layer on Y. All such distributions have their wave front sets in the normal bundle of Y which is a conic Lagrangian manifold. In Section 25.1 we generalize the notion of conormal distribution by defining the space of Lagrangian distributions associated with an arbitrary conic Lagrangian Λ ⊂ T*(X)\0. This is the space of distributions u such that there is a fixed bound for the order of P1, ... P N u for any sequence of first order pseudo-differential operators P1,...,PN with principal symbols vanishing on Λ. This implies that WF(u) ⊂ Λ. Symbols can be defined for Lagrangian distributions in much the same way as for conormal distributions. The only essential difference is that the symbols obtained are half densities on the Lagrangian tensored with the Maslov bundle of Section 21.6.