In this course we will carefully treat the fundamental aspects of crystal growth. We will study the thermodynamic prerequisites for crystal growth, such as chemical potential, construction of binary phase diagrams, supersaturation, and nucleation. Further on, we will discuss surface energies, surface diffusion, and Wulff’s theorem. In the course section on epitaxial growth we will discuss surface reconstructions, lattice mismatch, and dislocations, as well as characterization – both in- and ex-situ. We will also deal with growth techniques and reactor models. During the course, the various moments will be illuminated by examples from modern research, especially research on epitaxy of nanostructures.