  In this paper we present the enhanced X-ray Timing and Polarimetry mission -
eXTP. eXTP is a space science mission designed to study fundamental physics
under extreme conditions of density, gravity and magnetism. The mission aims at
determining the equation of state of matter at supra-nuclear density, measuring
effects of QED, and understanding the dynamics of matter in strong-field
gravity. In addition to investigating fundamental physics, eXTP will be a very
powerful observatory for astrophysics that will provide observations of
unprecedented quality on a variety of galactic and extragalactic objects. In
particular, its wide field monitoring capabilities will be highly instrumental
to detect the electro-magnetic counterparts of gravitational wave sources. The
paper provides a detailed description of: (1) the technological and technical
aspects, and the expected performance of the instruments of the scientific
payload; (2) the elements and functions of the mission, from the spacecraft to
the ground segment.
