  A high-energy $e^+e^-$ Linear Collider has been considered since a long time
as an important complement to the LHC. Unprecedented precision measurements as
well as the exploration of so far untouched phase space for direct production
of new particles will provide unique information to advance the limits of our
understanding of our universe. Within this project, the physics prospects of
such a collider as well as their interplay with design of the accelerator and
the detectors have been investigated in a quantitative way. This kind of study
required a close collaboration between theory and experiment, always taking
into account results of the LHC and other relevant experiments. In this article
we will summarize some of the most important developments and results, covering
all core areas of the physics progamme of future $e^+e^-$ colliders.
