Within the central 10 pc of our Galaxy lies a dense cluster of stars, the nuclear star cluster. This cluster forms a distinct component of our Galaxy. Nuclear star clusters are common objects and are detected in ~ 75% of nearby galaxies. It is, however, not fully understood how nuclear star clusters form. The Milky Way nuclear star cluster is the closest of its kind. At a distance of only 8 kpc we can spatially resolve its stellar populations and kinematics much better than in external galaxies. This makes the Milky Way nuclear star cluster the perfect local reference object for understanding the structure and assembly history of nuclear star clusters in general. There are of the order of 107 stars within the central 10 pc of the Galactic center. Most of these stars are several Gyr old late-type stars. However, there are also more than 100 hot early-type stars in the central parsec of the Milky Way, with ages of only a few Myr. Beyond a projected distance of 0.5 pc of the Galactic center, the density of young stars was largely unknown, since only very few spectroscopic observations existed so far. We covered the central >4 pc2 (0.75 sq.arcmin) of the Galactic center using the integral-field spectrograph KMOS (VLT). We extracted more than 1,000 spectra from individual stars and identified >20 new early-type stars based on their spectra. We studied the spatial distribution of the different populations and their kinematics to put constraints on the assembly history of the Milky Way nuclear star cluster.