Rechargeable batteries are of outstanding importance in achieving global climate goals as they play a key role in electronic applications, in the mobility sector for the electrification of cars, or stationary grid energy storage systems for surplus wind and solar power. The most prominent representatives are Lithium-ion batteries (LIBs) , which are facing controversy due to the use of critical raw materials such as lithium, cobalt, nickel, or graphite. Metallic lithium anodes have a high theoretical capacity (3861 mAh•g -1 ), the lowest negative electrochemical potential (-3.04 V vs. standard hydrogen electrode (SHE)), and a low density (0.59 g•cm -3 ), however, are prone to form dendrites. Dendrites are needle-shaped structures leading to short circuits, thermal runaways, and even battery failures, although promising approaches such as the electrostatic shielding of the lithium surface through additives have been proposed to tackle this problem. Due to these safety concerns, graphite with intercalated lithium ions is still used as anode material in commercial LIBs, reducing its theoretical capacity by roughly one order of magnitude to 372 mAh•g -1 in present day commercial LIBs. Therefore, rechargeable multivalent magnesium-ion batteries (MIBs) have emerged as a promising alternative, mainly due to the bivalency of the magnesium atom, which allows it to carry twice the charge resulting in a higher volumetric capacity (3833 mAh•cm -3 vs. 777 mAh•cm -3 of graphite anodes in commercial LIBs). Additionally, magnesium has a low electrochemical potential (-2.37 V vs. SHE), is highly abundant, of low cost, and is environmentally friendly. These benefits are reflected in the exponentially increasing number of publications that have recently been dedicated to the topic of MIBs, as shown in Figure from the publication by Li et al. On the other hand, a great deal of effort is required to find suitable electrolytes that allow reversible magnesium deposition while at the same time providing a broad electrochemical window. Conventional carbonate electrolytes cannot be used for rechargeable MIBs because the solid electrolyte interface (SEI) formed by decomposition products of the electrolyte is not permeable to magnesium-, in contrast to lithium-cations. Proposed solutions are electrolytes based on Grignard reagents, Mg(TFSI)2 salts or ionic liquids, as well as the use of polymeric interlayers as artificial SEI. Nevertheless, the structure and growth mechanism of SEI formation remains poorly understood due to its high complexity, highlighting the need for adequate theoretical modeling on different time and length scales. The second controversial issue is whether dendrite formation is possible on metallic magnesium anodes. On the one hand, the tendency of occurrence is significantly lower than for the lithium equivalent, yet dendrites have been demonstrated under harsh deposition conditions, as shown by the Banerjee group. As a result, there have been requests to conduct experiments to determine critical current densities and to define precise voltage windows for dendrite-free regions. In a recently published study, the critical overpotential of dendrite formation on lithium, sodium, and magnesium was calculated using a grandcanonical density functional theory (DFT) approach, indicating a combination of high surface tension, low surface capacitance, and low potential of zero charge (PZC) as indicators for mitigated dendrite growth. Another explanation for enhanced dendrite growth on lithium compared to magnesium surfaces includes the accumulation of negative excess charges at the peaks of protrusions of the lithium electrodes inducing a strong electric field that attracts further lithium cations. In addition, lower step-down and terrace self-diffusion barriers of magnesium compared to lithium are considered responsible for the reduced dendrite growth. In this work, periodic DFT calculations have been performed to determine the atomistic properties of magnesium and to explain the initial stages of surface growth. This technique has previously been applied for lithium and sodium in our group. For this purpose, the bulk, surface, and adsorption properties of magnesium were first calculated. Based on the obtained surface energies, the corresponding equilibrium shape of a magnesium crystal was determined within the framework of the Wulff construction. Subsequently, a wide variety of two-and three-dimensional diffusion processes on perfect and imperfect Mg(0001) and Mg(101 ! 1) surfaces were investigated and analyzed concerning surface growth phenomena.