  In this paper, we analyze various types of critical phenomena in
one-dimensional gas flows described by Euler equations. We give a geometrical
interpretation of thermodynamics with a special emphasis on phase transitions.
We use ideas from the geometrical theory of PDEs, in particular, symmetries and
differential constraints to find solutions to the Euler system. Solutions
obtained are multivalued, have singularities of projection to the plane of
independent variables. We analyze the propagation of the shock wave front along
with phase transitions.
