In this Lecture, we start with the second-order correction to the ion–ion interactionInteractionion–ion interaction and analyze the emergence of sound in metalsSoundsound in metal. We consider the energy functional and determine the volume and the structure (the shape) of elementary cellCellelementary cell in metals as a function of the correlation radius. We discuss the energy balance in metallic hydrogenHydrogenmetallic hydrogen and the critical pressureCriticalcritical pressurePressurecritical pressure required for the stabilization of the atomic metal phase. We advocate the vibrational spectrum for the highly anisotropic filamentous metastable phasePhasemetastable phase of metallic hydrogenHydrogenmetallic hydrogen formed by one-dimensional proton filamentsFilamentproton filament embedded in the three-dimensional electron Fermi liquid. We present the estimate for the lifetime of the metastable phasesPhasemetastable phase related to the under-barrier tunnelingTunnelingunder-barrier tunneling and growth of the critical seed of the molecular phase in the configurational space.