Hydrogen under ambient pressure and low temperature forms a molecular crystal which under high pressure of ~400 GPa is predicted turn into metal and at further compression up to ~500 GPa hydrogen molecules dissociate and are transformed to a monoatomic crystal. This simplest metal is predicted to be a superconductor with a very high critical temperature Tc ~200 K. Moreover, this superconductor might be recovered to ambient pressure. Metallic hydrogen might acquire a new quantum state, namely the metallic superfluid and the superconducting superfluid. Because the zero-point motions of the hydrogen nuclei (protons) are significant, they might stabilize metallic hydrogen in a zero-temperature liquid ground state similar to liquid helium. For this state, superconductivity for electrons and protons (Fermi-liquids) is expected in hydrogen, and superconductivity for electrons and superfluidity for deutrons in deuterium (an isotope of hydrogen). For astrophysics the study of metallic hydrogen is important because it might be a main constituent in giant planets and stars.We plan to explore three directions to achieve and study metallic hydrogen: (a) Compression of pure hydrogen at room and lower temperatures to record pressures of 440 GPa which we currently achieve (b) Exploration of the higher temperature domain P> 150 GPa, T<1000 K; (c) Study of hydrogen dominant materials at low pressures P>50 GPa and low temperatures. We will give first preference to compression pure hydrogen to metallic state at low temperatures to verify the theoretical prediction in the region of ~ 400 GPa. In case this pressure would not be sufficient our study will be focused on parallel tasks hydrogen dominant materials, and fluid hydrogen.