This thesis is devoted to the study of integrable quantum systems such as spin chains, two-dimensional field theories and the AdS/CFT duality. This AdS/CFT duality is a conjecture, stated in the end of the last century, which relates (for instance) the non- perturbative regime of a superconformal gauge theory (called N =4 super Yang-Mills) and the perturbative regime of a string theory on a 10-dimensional space with the geometry AdS5×S5 . This thesis explores the similarities between integrable spin chains and quantum field theories, such as Super Yang Mills. We first study integrable spin chains and build explicitly a polynomial "Bäcklund flow" and polynomial "Q-operators", which allow to diagonalize the Hamiltonian. We then study integrable field theories et show how to obtain "Q-functions", analogous to the Q-operators built for spin chains. It turns out that several important informations are contained in the analytic properties of these Q-functions. That allows to obtain, in the framework of the thermodynamic Bethe ansatz, a finite number of non-linear integral equations encoding the spectrum of the theory which we study. This system of equations is equivalent to an infinite system of equations, known as "Y-system", which had been quite recently conjectured in the case of the AdS/CFT duality.
