[en] Optical frequency comb technology has been used in this work for the first time to investigate the nuclear structure of light radioactive isotopes. Therefore, three laser systems were stabilized with different techniques to accurately known optical frequencies and used in two specialized experiments. Absolute transition frequency measurements of lithium and beryllium isotopes were performed with accuracy on the order of 10^-10. Such a high accuracy is required for the light elements since the nuclear volume effect has only a 10^-9 contribution to the total transition frequency. For beryllium, the isotope shift was determined with an accuracy that is sufficient to extract information about the proton distribution inside the nucleus. A Doppler-free two-photon spectroscopy on the stable lithium isotopes ^6,7Li was performed in order to determine the absolute frequency of the 2S → 3S transition. The achieved relative accuracy of 2 x 10^-10 is improved by one order of magnitude compared to previous measurements. The results provide an opportunity to determine the nuclear charge radius of the stable and short-lived isotopes in a pure optical way but this requires an improvement of the theoretical calculations by two orders of magnitude. The second experiment presented here was performed at ISOLDE/CERN, where the absolute transition frequencies of the D₁ and D₂ lines in beryllium ions for the isotopes ^7,9,10,11Be were measured with an accuracy of about 1 MHz. Therefore, an advanced collinear laser spectroscopy technique involving two counter-propagating frequency-stabilized laser beams with a known absolute frequency was developed. The extracted isotope shifts were combined with recent accurate mass shift calculations and the root-mean square nuclear charge radii of ^7,10Be and the one-neutron halo nucleus ¹¹Be were determined. Obtained charge radii are decreasing from ⁷Be to ¹⁰Be and increasing again for ¹¹Be. While the monotone decrease can be explained by a nucleon clustering inside the nucleus, the pronounced increase between ¹⁰Be and ¹¹Be can be interpreted as a combination of two contributions: the center-of-mass motion of the ¹⁰Be core and a change of intrinsic structure of the core. To disentangle these two contributions, the results from nuclear reaction measurements were used and indicate that the center-of-mass motion is the dominant effect. Additionally, the splitting isotope shift, i.e. the difference in the isotope shifts between the D₁ and D₂ fine structure transitions, was determined. This shows a good consistency with the theoretical calculations and provides a valuable check of the beryllium experiment. (orig.)