This research monograph provides a pedagogical and self-contained introduction to non-equilibrium quantum particle dynamics for inhomogeneous systems, up to and including a survey of recent breakthroughs pioneered by the authors and other groups. The theoretical approach is based on real-time Green’s functions (Keldysh Green’s functions), directly solving the two-time Kadanoff-Baym equations (KBE). This field has seen a rapid development over the last decade, with new applications emerging in plasma physics, semiconductor optics and transport, nuclear matter and high-energy physics.  This text will be a valuable starting point and reference work for graduate students and researchers interested in the quantum dynamics of inhomogeneous systems.