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[en] Optical measuring methods allow the detection and identification of the atomic structure with extraordinary precision. Deviations to theoretical predictions can indicate unknown physical effects. Therefore, precise measurements on the atomic structure continue to be of large relevance. In this work, a laser system for precision spectroscopy on Bismuth ("2"0"9Bi"8"2"+), Tellurium ("1"3"0Te_2) and Rydberg states of Rubidium ("8"5Rb) has been built and characterized. Spectroscopic measurements on Tellurium and Rubidium have been achieved with this setup. The system consists of a two-stage frequency doubled diode laser, stabilized via a cavity and an RF-offsetlock to arbitrary wavelengths with absolute high stability. The setup of the laser system will be presented and the systematic error caused by the refractive index of air inside the transfer cavity will be discussed. A stability of better then 6.14 MHz at 244 nm is obtained for planned experiments on the ground state hyperfine splitting of "2"0"9Bi"8"2"+. This will allow an increase in precision of more then four orders of magnitude for this measurement. Further increase in precision can be achieved by using an evacuated cavity. The obtained stability is measured by comparison of the laser frequency to absorption lines of Tellurium ("1"3"0Te_2). Eight reference lines, known from literature, spanning the region from 613720.717 GHz to 616803.545 GHz have been measured. The frequency measurements of three lines, coinciding with the emission spectrum of an argon-ion-laser, show deviations with respect to the published frequencies. Further inconsistencies in literature are cleared. Part of this work is also the precise measurement of 843 Doppler-free "1"3"0Te_2 reference lines spanning the frequency range from 613881.150 GHz to 616614.258 GHz at a precision of better then 4 MHz for most lines. Additionally, measurements on electromagnetically induced transparency (EIT) using Rydberg transitions of Rubidium have been achieved. Recorded spectra of the transitions to the principal quantum numbers n=20, 58, 79, 97 and 150 are shown. This proofs the applicability of the built laser sys- tem to the full range of two-photon Rydberg excitation of Rubidium. When the ground, intermediate and exited state are varied, the resulting spectrum of resonances is explained and analysed representatively on the transition to the Rydberg D-states of "8"5Rb with n = 97. The energy shift of the atomic levels by both electric and magnetic fields are examined. By measuring the two photon transition frequency of 5 "2S_1_/_2 → 150 "2D_5_/_2, the ionization energy of 85 Rb is redetermined.