The ASACUSA (Atomic Spectroscopy And Collisions Using Slow Antiprotons) collaboration at CERN will perform an experiment using Rabi's magnetic resonance method to measure the frequencies of ground state hyperfine transitions of antihydrogen. Since antihydrogen is the CPT symmetric partner of hydrogen and the frequency of these transitions in hydrogen are very well known, such measurements will provide a very sensitive test of CPT symmetry. To prepare and characterize the spectroscopy apparatus for measurements with antihydrogen atoms, measurements with hydrogen atoms are performed. A beam of atomic hydrogen is used instead of the ASACUSA antihydrogen source, and a quadrupole mass spectrometer instead of an annihilation detector. A hyperfine spectroscopy apparatus (consisting of a cavity tuned to measure one of the two possible transitions, the -transition, and a superconducting sextupole magnet) has already been commissioned and is currently in operation at the ASACUSA antihydrogen hyperfine structure experiment at CERN. In this work a second cavity is prepared, which enables simultaneous measurement of the two possible transitions, the - and TT transition. For operation with hydrogen the superconducting sextupole magnet is replaced by permanent sextupole magnets, which are built and characterized in the course of this work. The velocity and state selection properties of a sextupole doublet are simulated and measured. Numerical simulations of trajectories of hydrogen atoms in the spectroscopy apparatus are performed to obtain a quantitative understanding of the beam transport. These simulations lead to a new beam optics, based on ring apertures, which is implemented and tested. Finally, the and TT hyperfine transitions of ground state hydrogen are measured with the spectroscopy apparatus in earth's magnetic field.