  We consider the classical compressible Euler's Equations in three space
dimensions with an arbitrary equation of state, and whose initial data
corresponds to a constant state outside a sphere. Under suitable restriction on
the size of the initial departure from the constant state, we establish
theorems which give a complete description of the maximal development. In
particular, the boundary of the domain of the maximal solution contains a
singular part where the inverse density of the wave fronts vanishes and the
shocks form. We obtain a detailed description of the geometry of this singular
boundary and a detailed analysis of the behavior of the solution there.
