Laser-ablated Mg atoms react with molecular hydrogen to give magnesium hydrides during condensation in excess hydrogen and neon for characterization by matrix infrared spectroscopy. The observed absorptions are identified by isotopic substitution and theoretical calculations of vibrational fundamentals and assigned to the MgH, MgH2, Mg2H, Mg2H2, Mg2H3, and Mg2H4 Molecules. Subsequent UV irradiation excites Mg to the P-1 state, which inserts into H-2 and markedly increases the yield of MgH2 and Mg2H4. Interesting MgH2(H-2), complexes are formed with high yield in solid hydrogen. Mg2H4 is a dibridged molecule analogous to dialane. Sample annealing gives MgH2 polymers, which favor single bridge-bond linkages. Warming above 8 K allows the H-2 matrix to evaporate and solid MgH2 to form with broad 1160 and 560 cm(-1) absorptions that remain on the window at 300 K. Thus, we have reacted the elements to give the stable MgH2 molecule, formed its dimer and tetramer, and finally obtained the ultimate polymer, solid MgH2, which is of interest for hydrogen storage.