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A measurement of the 1s-2s energy splitting by Doppler-free twc+photon spectroscopy yields a value of 2 455 529 002 (33)(46) MHz, which agrees with QED theory within two standard deviations. The mass of the positive muon is derived as 105.658 80 (29) (43) MeV/c2 from the isotope shifts in this transition to hydrogen and deuterium.One-electron atoms, being the most fundamental atomic systems, provide excellent tests for bound state quantum electrodynamics (QED) and render the possibility of highly precise measurements of fundamental constants. As the energy levels of the natural hydrogen isotopes (hydrogen, deuterium and tritium) and hydrogen-like exotic systems with hadronic nuclei (e.g. muonic helium, pionium and many others) are influenced by the finite size and internal structure of the hadrons, the interpretation of highly precise measurements in such systems is limited by todays insufficient knowledge of the nuclear size effects. The hydrogen-like muonium atom (p+e-) consists of two leptons from two different generations [l]. No internal structure is known for leptons down to dimensions of order m; therefore muonium is free from nuclear structure effects. The level energies can be calculated to very high accuracy exclusively by the theory of bound state Quantum Electrodynamics (QED). The potential for high precision studies has been demonstrated in a long series of microwave measurements and theoretical calculations of the ground state hyperfine structure splitting [l], from which accurate values for fundamental constants (muon mass m,, and fine structure constant a) were obtained [l]. The optical 1s-2s transition offers a higher resolution than the ground state hyperfine structure splitting, because of the much higher transition frequencies (and QED contributions) and the same 144 kHz narrow linewidth, which is due to the muon lifetime r,,=2.2psec.This experiment was performed at the worlds Figure 1: Laser system employed in the experiment.brightest pulsed surface muon source at the Rutherford Appleton Laboratory (RAL) in Chilton, UK. The 12S1,2(F=1) --+ 22S1/2(F=1) transition was induced by Doppler-free two-photon laser spectrcscopy using two counter-propagating laser beams of wavelength X = 244 nm [2]. The atoms were formed by electron capture after stopping positive muons close to the surface of a Si02 powder target. 246