Additive manufacturing (AM) of metals offers highest production flexibility, almost unlimited freedom of design and the potential for pointwise control of microstructure and mechanical properties. However, a sub-optimal choice of process parameters often leads to high residual stresses, dimensional warping, porosity, undesirable microstructures or even failure of the part during production. The main objective of this course is to convey the physical fundamentals of metal AM processes, the basics of process implementation and monitoring, material aspects as well as modeling and simulation techniques on different length scales. The course begins with an overview of existing metal AM processes comprising powder bed fusion additive manufacturing (PBFAM), e.g. selective laser melting (SLM), selective laser sintering (SLS), electron beam melting (EBM), directed energy deposition (DED), binder jetting (BJ), and material droplet printing (MDP). After conveying the physical fundamentals, potential fields of application and the technical implementation, means of monitoring and process control are presented. Different types of defects in metal AM are categorized and strategies for defect detection via in-situ and ex-situ metrology (e.g. X-Ray computer tomography CT, density inspection, geometry control) are discussed. Moreover, the course will convey essential material aspects such as the principles, mechanisms and kinetics of solidification as well as the fundamentals of equilibrium and non-equilibrium thermodynamics. Phase formation and microstructure control, alloy design, powder metallurgy and process-microstructure-property correlations will be discussed in the context of metal AM and compared to conventional casting. A further focus of the course lies on modelling and simulation approaches in metal AM, covering the underlying modelling assumptions, governing equations, discretization strategies as well as numerical aspects (e.g. balance of computational efficiency and solution accuracy). Specifically, modelling strategies for the mechanics, radiation transfer, heat transfer and sintering kinetics in powder beds are discussed. Moreover, mesoscale thermo-hydrodynamics modelling and simulation approaches aiming at the prediction of melt flow instabilities and final part properties such as surface roughness, layer-to-layer adhesion and residual porosity are conveyed. Eventually, part-scale thermo-solid-mechanics modelling and simulation approaches aiming at the prediction of residual stresses, thermal strains, constitutive behavior and dimensional warping at the length scale of entire design parts are presented. Each set of lectures will start from the respective basics but will then quickly move on to cutting-edge research topics. The lectures are primarily designed for doctoral students of mechanics, engineering, material sciences and physics with a strong interest in the different research aspects of metal AM. However, they are equally suited for young and senior researchers, who would like to gain a comprehensive overview in an efficient compact course format. It might also be interesting for practicing engineers working on high-level industrial applications of metal AM.