Trapped atomic ions can represent elementary quantum systems that are well isolated from the environment. They can be brought nearly to rest by laser cooling and both their internal electronic states and external motion can be coupled to and manipulated by light fields. This makes them ideally suited for studies in quantum optics, quantum dynamics and quantum information processing. This lecture covers the physics of confinement in ion traps, the coupling of ions to laser fields, laser cooling of single ions and ion crystals, sympathetic cooling between different ion species and near ground-state transport, separation and recombination of ions.