This book covers a new approach to analyzing hydrodynamic stability. With the use of standard remedies of functional analysis, theory of boundary value problems and infinitesimal Lie algebras, it is shown in the book that large vortex mushrooms of an ideal incompressible fluid in a vertical strip behind a water hammer proves to be 2D (plane-parallel) nonlinear (for arbitrary disturbances of initial velocities) and long wave stable. It is one of the many examples provided in the book discussing hydrodynamic stability.