Infrared magneto-absorption has been investigated in thin samples (~10 microns) of germanium, indium arsenide, and indium antimonide in magnetic fields up to 37 kilogauss. At photon energies greater than the direct transition energy gap in germanium and also greater than the energy gaps in indium arsenide and indium antimonide, the magneto-absorption exhibited oscillatory behavior. This is associated with interband transitions between quantized Landau levels of the valence and conduction bands. By extrapolating a plot of the photon energies of the transmission minima as a function of magnetic field to zero field, we obtained accurate determinations of the energy gaps. For the direct transition in germanium, Eg=0.803+/-0.001 ev at ~298°K, 0.890+/-0.001 ev at ~77°K, and 0.897+/-0.001 ev at ~4°K. In indium antimonide, Eg=0.180+/-0.002 ev at ~298°K, and in indium arsenide, the result was 0.360+/-0.002 ev at ~298°K. From the accurate determination of the energy gap made possible by these experiments, it is apparent that there is considerable absorption below the energy gap, probably due to transitions involving both photons and optical phonons. Utilizing the theory of Luttinger and Kohn, effective masses were evaluated from the higher quantum transitions in germanium to give values of the conduction band electron mass at k=0 of (0.036+/-0.002)m0 at room temperature, and (0.043+/-0.002)m0 and (0.041+/-0.002)m0 at ~77°K and ~4°K, respectively, which is consistent with the corresponding change in energy gap. For indium arsenide, the conduction band electron mass was found to be approximately 0.03m0. For indium antimonide, a value for the effective mass in the conduction band of ~0.014m0, consistent with the cyclotron resonance results, was obtained by assuming that in this case the magnetic levels in the conduction band are appreciably split by spin-orbit interaction. The anisotropy of the magneto-absorption effect was measured for germanium and indium antimonide. For germanium, the anisotropy agreed with predictions from theory and the results of microwave cyclotron resonance. For indium antimonide, the anisotropy was very small for the first two minima.