In this series of three lectures I will discuss nonlinear quantum hydrodynamics in quantum electronic liquids. I will concentrate on three of the most important systems: – Degenerate Fermi gas in one spatial dimension, – Edge state in the Fractional Quantum Hall Effect, – Luttinger Liquid. par I will discuss: – why Fermi statistics causes nonequilibrium quantum liquids to be essentially nonlinear, – instabilities and singularities arising as a result of nonlinear nature of quantum liquids, – mathematical methods for analysis of singularities in dynamics of quantum liquids, – relation to random matrix theory and to perturbed conformal field theory.

Univ. of Chicago