This thesis reports on the study of elementary reactions of the carbon radicals C, C2 and C3 at combustion temperatures. The shockwave technologie was used to generate the necessary gas temperatures of 2500 K up to 5000 K. Fast optical measurement techniques were applied for the time resolved observation of radical reactions. For the detection of C2-radicals, a highly sensitive diagnostic was developed, based on a ring-dye-laser spectrograph. The radicals C3 and CN and the atomic species C, N, and O were measured with a CCD-Camera spectrograph and with the atomic-resonance-absorption spectroscopy. The thermal decomposition (pyrolysis) of acetylene (C2H2) was used as a source for Carbon radicals. Results of this thesis are an extension and a verification of reaction mechanisms for the pyrolysis of acetylene as well as the determination of rate coefficients for the decompostion reactions of C2H2, C2H and C2 and for the bimolecular reactions of C2 with H2, O, O2, N2 and NO.