Future e+e- Linear Colliders offer the potential to explore new physics at the TeV scale to very high precision. The lecture series introduces the possibilities of a TeV linear collider (the International Linear Collider, ILC) in the fields of Higgs physics, alternative Electro-weak Symmetry Breaking scenarios, Supersymmetry, Extra Dimensions, and more exotic models. Also the prospects for highly improved measurements of SM parameters such as the top quark mass and electro-weak gauge boson properties are discussed. The implications for the design of an appropriate detector are outlined and current R&D developments are explained. Particular emphasis will be given to the complementarity and intimate interplay of physics at the LHC and the ILC. The additional benefit of multi-TeV e+e- collisions as envisaged in the CLIC project are discussed.
