An experimental and numerical investigation of boundary layer suction (BLS) on a transonic compressor blade has been conducted. The objective of the present work is to identify the possible benefit of boundary layer suction via a slot in the region of the shock/boundary layer interaction (SBLI). The study has two major parts: First, an investigation of the flow on an isolated airfoil without and with BLS on the suction side (SS). This investigation is intended to optimise the suction slot geometry in terms of location and width. Second, a study on a transonic cascade with supersonic inlet flow has been conducted with the goal to show the influence of the BLS on the pressure loss coefficient and the surface Mach number distribution. An initial literature study revealed that only few work has been carried out in the field of BLS in transonic compressors and no data close to the suction slot was available. The main steps of the present study are: The design of an isolated airfoil for testing in a Laval nozzle, representative for the flow at a compressor root section, with enough space inside to evacuate the aspirated air. A numerical study of the flow on the isolated airfoil without and with BLS on the SS . An experimental investigation of the isolated airfoil without and with BLS on the SS using static surface pressure taps, PSP and the Schlieren method for data acquisition. Design and numerical investigation of a suitable transonic compressor cascade with enough space inside to evacuate the suction mass flow. An experimental investigation of the designed transonic cascade with an inlet Mach number of 1.23 with two sets of blades in the non-rotating annular cascade test-rig; one without and one with BLS at 40% chord. The main results are: The numerical study of the flow on the isolated airfoil without and with BLS on the SS shows, that the onset of shock-induced separation could be shifted to an increased inlet Mach number. Steady 2D-NS simulations show that the reference configuration exhibits an attached flow behind the shock up to an inlet Mach number of up to 0.70 for an inlet flow angle of +4°. The configuration with BLS shows attached flow behind the shock for an an inlet Mach number of 0.725. Unsteady 2D-NS simulations show for an inlet flow angle of +4° at an inlet Mach number of 0.725 for the reference configuration a shock, which moves periodically on the SS due to a separated boundary layer created by the shock/boundary layer interaction. The same configuration with BLS shows a stable shock position. The experimental investigation of the isolated airfoil without and with BLS on the SS shows that BLS at 15% chord upstream of the initial shock location for an inlet Mach number of 0.725 at a flow angle of +4° leads to a shock location 10% chord downstream of the initial position. Boundary layer suction suppresses flow separation and stabilises the shock. Due to the suction a stagnation point is created at the downstream edge of the suction slot. Downstream of this stagnation point, the flow is re-accelerated to the isentropic Mach number level of the reference configuration without BLS. The design and 3D-numerical investigation of a suitable transonic compressor cascade shows, that BLS with a suction mass flow of 2% can increase the maximum pressure ratio and diffusion factor of approximately 10%. This is the consequence of the stabilisation of the shock in the blade passage due to the suction. The experimental investigation of the designed transonic cascade with an inlet Mach number of 1.23 with 2% suction mass flow shows, that BLS acts locally and that suction leads to an increased isentropic surface Mach number in front of the suction slot and due to the suction related stagnation point, to a locally decreased velocity immediately downstream of the suction slot. Then the flow re-accelerates to the same level as the non-suction configuration attains. The pressure loss coefficient is decreased by up to 3.6% for the most positive incidences. The results of this investigation confirm that boundary layer suction on the suction side of an airfoil is a suitable way to increase the working range of a compressor as the shock position can be stabilised (shock-trapping) and the increase of the pressure loss coefficient can be shifted to higher incidences.