These refereed proceedings present recent developments on specific mathematical and physical aspects of nonlinear dynamics. The new findings discussed in here will be equally useful to graduate students and researchers. The topics dealt with cover a wide range of phenomena: solitons, integrable systems, Hamiltonian structures, Backlund and Darboux transformation, symmetries, fi- nite-dimensional dynamical systems, quantum and statistical mechanics, knot theory and braid group, R-matrix method, Hirota and Painleve analysis, and applications to water waves, lattices, porous media, string theory...