The mechanism by which negative μ mesons catalyze nuclear reactions between hydrogen isotopes is studied in detail. The reaction rate for the process (p+d+μ--->He3+μ-+5.5 Mev), observed recently by Alvarez et al., is calculated and found to be in accord with the available data. The μ- meson binds two hydrogen nuclei together in the μ-mesonic analog of the ordinary H+2 molecular ion. In their vibrational motion the nuclei have a finite, although small, probability of penetrating the Coulomb barrier to zero separation where they may undergo a nuclear reaction. The intrinsic reaction rates for other, more probable, reactions are also estimated. The results are ~0.3×106 sec-1 for the observed p-d reaction, ~0.7×1011 sec-1 for the d-d reaction, and ~0.4×1013 sec-1 for the d-t reaction. For the reaction observed by Alvarez rough estimates are made of the partial widths for nonradiative and radiative decay of the excited He3 nucleus. The ejection of the μ- meson by "internal conversion" seems somewhat less likely. Speculations are made on the release of useful amounts of nuclear energy by these catalyzed reactions. The governing factors are not the intrinsic reaction rate once the molecule is formed, but rather the time spent (~10-8 sec) by the μ- meson between the breakup of one molecule and the formation of another and the loss of μ- mesons in "dead-end" processes. These factors are such that practical power production is unlikely. In liquid deuterium, each μ- meson will catalyze only ~10 reactions in its lifetime, while for the d-t process it will induce ~100 disintegrations. A longer lived particle will not be able to catalyze appreciably more reactions.