The discovery of dark matter in galaxies marks a turning point in astrophysics

especially because of its conceptual relevance to cosmology. After a brief introduction to the dynamics of collisionless stellar systems, a short account is given of the study of dark halos in ellipticals. Then it is shown that the dark matter contained in galaxies does not change the value of the key cosmological parameters significantly. The text continues with an outline of some modern simulations of structure formation, a vast and fast-evolving field of research that ultimately focuses on the issues that define the formation and the evolution of galaxies and on the structure of dark halos. Then, at the forefront of current research, for the nearby and present universe the potential of modern telescopes such as Gaia is briefly recalled; for the distant and early universe, a short summary is given of the role of gravitational lensing as diagnostics of dark matter for galaxies, clusters of galaxies, and structure formation. Finally, the main steps are outlined of an attempt (MOND), started in the early 1980s and still continuing with some success, which explores the possibility that the law of gravitation requires a modification on the scales of galaxies and beyond and that dark matter does not exist.