We apply the Similarity Renormalization Group (SRG) method to quantum dots, using the same methodology that has recently had great success in the nuclear physics community. The SRG method can be realized in two different ways: In free space with respect to the physical vacuum state, or in-medium using the particle-hole formalism of second quantization. We start with the free-space approach, which is computationally less effective but has the advantage that no truncation occurs. We analyse the ground state using two different generators, Wegner's canonical generator and a modified version of that one, and meet numerical problems by replacing the standard Coulomb by an effective interaction and the harmonic oscillator by a Hartree-Fock basis. Afterwards, we apply the recently evolved in-medium SRG approach to our electronic systems. Here we choose the IM-SRG(2) method, meaning that all operators are truncated on a two-body level. Again, we apply two different generators, Wegner's canonical generator and White's generator. We demonstrate that Wegner's generator leads to numerical instabilities and stiff equation systems, especially for systems with comparatively high correlations. Computations with White's generator, on the other hand, are shown to be much more efficient and require less CPU time, especially as the size of the basis is increased. This enables us to look at systems up to N=42 particles. To analyse the capabilities of IM-SRG(2), we compare our results for the ground state energy with other ab-initio many-body methods, including Hartree-Fock, Coupled Cluster, Diffusion Monte Carlo and Full Configuration Interaction. Finally, we use the IM-SRG(2) results to study the role of correlations in two-dimensional quantum dots.