[en] Recent experiments have shown that under proper conditions a single muon may catalyze almost two hundred fusions in its lifetime. This process proceeds through formation of muonic molecular ions. Properties of these ions are central to the understanding of the phenomenon. Our work included the most accurate calculations of the energy levels and Coulombic sticking fractions for tdμ and other muonic molecular ions, calculations of Auger transition rates, calculations of corrections to the energy levels due to interactions with the most molecule, and calculation of the reactivation of muons from α particles. The majority of our effort has been devoted to the theory and computation of the influence of the strong nuclear forces on fusion rates and sticking fractions. We have calculated fusion rates for tdμ including the effects of nuclear forces on the molecular wave functions. We have also shown that these results can be reproduced to almost four digit accuracy by using a very simple quasifactorizable expression which does not require modifications of the molecular wave functions. Our sticking fractions are more accurate than any other theoretical values. We have used a more sophisticated theory than any other work and our numerical calculations have converged to at least three significant digits