Dominating finite-range interactions in many-body systems can lead to intriguing self-ordered phases of matter. Well known examples are crystalline solids or Coulomb crystals in ion traps. In those systems, crystallization proceeds via a classical transition, driven by thermal fluctuations. In contrast, ensembles of ultracold atoms laser-excited to Rydberg states provide a well-controlled quantum system [1], in which a crystalline phase transition governed by quantum fluctuations can be explored [2][3][4]. Here we report on the experimental preparation of the crystalline states in such a Rydberg many-body system. Fast coherent control on the many-body level is achieved via numerically optimized laser excitation pulses [2][3][4]. We observe an excitation-number staircase [2][3][4][5][6][7] as a function of the system size and show directly the emergence of incompressible ordered states on its steps. Our results demonstrate the applicability of quantum optical control techniques in strongly interacting systems, paving the way towards the investigation of novel quantum phases in long-range interacting quantum systems, as well as for detailed studies of their coherence and correlation properties [2][3][4][5][6][7][8].Rydberg atoms exhibit unique properties that are key to realize and explore novel quantum many-body Hamiltonians and their phases. The strong van der Waals interaction between them allows to create many-body systems with tailored long-range interactions in neutral ultra-cold atom samples [1,9,10]. Complete experimental control of these systems is possible using the well developed toolbox of quantum optics for the laserexcitation to the Rydberg states. The magnitude of the resulting interactions between the Rydberg atoms is determined by the choice of the excited state and it can exceed all other relevant energy scales on distances of several microns, thereby leading to an ensemble dominated by long-range interactions. In this regime, the ground state of the resulting many-body system is expected to show crystalline ordering of the Rydberg excitations, which can be understood in the limit of vanishing coupling as the classical closest packing of hard spheres [11]. The lattice constant of the crystal is set by the dipole blockade radius R b [12,13], defined as the inter-particle spacing at which the dipole interaction between two Rydberg atoms exceeds the spectral range of the optical coupling. To prepare the system in this crystalline phase, a dynamical approach has been suggested that adiabatically connects the ground state containing no Rydberg excitations with the targeted crystalline state. At the heart of this dynamical crystallization technique is the coherent control of the many-body system [2][3][4][14][15][16][17].Previous experiments showed direct or indirect evidence for correlations caused by the long-range interac- * Electronic address: peter.schauss@mpq.mpg.de tions in Rydberg many-body systems, such as a universal scaling of the Rydberg excitation number [18], subPoissonian counting statis...