  This review is devoted to the classical integrability of the AdS5xS5
superstring theory. It starts with a reminder of the corresponding action as a
coset model. The symmetries of this action are then reviewed. The classical
integrability is then considered from the lagrangian and hamiltonian points of
view. The second part of this review deals with the gauge fixing of this
theory. Finally, some aspects of the pure spinor formulation are also briefly
reviewed.
