Antihydrogen is the simplest atom consisting entirely of antimatter. Since its counterpart hydrogen is one of the best studied atoms in physics, a comparison of antihydrogen and hydrogen offers one of the most sensitive tests of CPT symmetry. CPT, the successive application of charge conjugation, parity and time reversal transformation is a fundamental symmetry conserved in the standard model (SM) of particle physics as a consequence of a mathematical theorem. These conditions for this theorem to be fulfilled are not valid any more in extensions of the SM like string theory or quantum gravity. Furthermore, even a tiny violation of CPT symmetry at the time of the big bang could be a cause of the observed antimatter absence in the universe. Thus the observation of CPT violation might offer a first indication for the validity of string theory, and would have important cosmological consequences.This project proposes to measure the ground state hyperfine (HFS) splitting of antihydrogen (HBAR), which is known in hydrogen with relative precision of 10^–12. The experimental method pursued within the ASACUSA collaboration at CERN-AD consists in the formation of an antihydrogen beam and a measurement using a spin-flip cavity and a sextupole magnet as spin analyser like it was done initially for hydrogen. A major milestone was achieved in 2010 when antihydrogen was first synthesized by ASACUSA. In the first phase of this proposal, an antihydrogen beam will be produced and the HBAR-HFS will be measured to a precision of around 10^–7 using a single microwave cavity. In a second phase, the Ramsey method of separated oscillatory fields will be used to increase the precision further. In parallel methods will be developed towards trapping and laser cooling the antihydrogen atoms. Letting the cooled antihydrogen escape in a field free region and perform microwave spectroscopy offers the ultimate precision achievable to measure the HBAR-HFS and one of the most sensitive tests of CPT.