1. Although the present notes on integrability detectors can stand by themselves the reader can find a wealth of information on integrable systems, as well as a detailed bibliography, in the book of M.J. Ablowitz and P.A. Clarkson Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, 1992.
2. H. Poincaré, Les méthodes nouvelles de la Mécanique Céleste, Gauthier Villars, Paris (1892).
3. S. Novikov, Math. Intel. 14 (1992) 13.
4. We refer here to the famous Kolmogorov-Arnold-Moser (KAM) theorem and its applications in the study on near-integrable systems.
5. H. Segur, Physica D51 (1991) 343. We must point out here that the title of this section has been anashamedly stolen from this article of Segur.