Shocks Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics 1 Amplitude equations for weakly nonlinear surface waves in variational problems 2 Global weak solutions of PDEs for compressible media: A compactness criterion to cover new physical situations 3 Second microlocalization and stabilization of damped wave equations on tori 4 A few remarks on hyperbolic systems with Zygmund in time coefficients 5 Well posedness of linearized Taylor equations in magnetohydrodynamics 6 Strictly dissipative non uniqueness with corners 7 On the solvability of certain degenerate partial differential operators 8 Location and Weyl formula for the eigenvalues of some non self adjoint operators 9 A microscopic point of view on singularities in fluid models 10 Geometric optics for Rayleigh pulses in nonlinear elasticity 11 Recent results on stability of planar detonations The book collects the most relevant results from the INdAM Workshop Shocks Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics held in Rome September 14 18 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems addressing general theoretical issues such as symmetrizability singularities low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant such as nonlinear optics shock theory (stability relaxation) and fluid mechanics (boundary layers water waves Euler equations geophysical flows etc.). It is a valuable resource for researchers in these fields