  In this account we investigate an asymptotically flat space-time geometry. In
particular, we focus on a pure gravity model with cylindrical symmetry where no
matter fields are included. The Einstein-Rosen metric is introduced and the
corresponding Einstein equations are solved. By use of the ADM formalism, we
derive the observables of the cylindrical gravitational waves. We conclude with
an analysis of the algebra of the observables of the Einstein-Rosen waves.
