The Universe is permeated by hot, turbulent, magnetized plasmas. Turbulent plasma is a major constituent of active galactic nuclei, supernova remnants, the intergalactic and interstellar medium, the solar corona, the solar wind and the Earth's magnetosphere, just to mention a few examples. Energy dissipation of turbulent fluctuations plays a key role in plasma heating and energization, yet we still do not understand the underlying physical mechanisms involved. THOR is a mission designed to answer the questions of how turbulent plasma is heated and particles accelerated, how the dissipated energy is partitioned and how dissipation operates in different regimes of turbulence. THOR is a single-spacecraft mission with an orbit tuned to maximize data return from regions in near-Earth space - magnetosheath, shock, foreshock and pristine solar wind - featuring different kinds of turbulence. Here we summarize the THOR proposal submitted on 15 January 2015 to the 'Call for a Medium-size mission opportunity in ESAs Science Programme for a launch in 2025 (M4)'. THOR has been selected by European Space Agency (ESA) for the study phase. ; Funding: The THOR science team thanks the Swedish National Space Board for support to carry out a technical assessment phase study before the proposal submission. We acknowledge the useful discussion and comments from the THOR team (http://thor.irfu.se/team) and particularly D. Delcourt, D. Fontaine, A. Kis, G. Lapenta, M. Maksimovic, M. Opher, G. Paschmann, A. Petrukovic, S. Schwartz. We acknowledge: the support of the UK Space Agency through grant ST/N003322/1 to ICL; the support of Agenzia Spaziale Italiana through contract ASI-INAF 2015-039-R.O to University of Calabria, Italy and at IAPS/INAF, Rome; the support of the Belgian Science Policy Office through PRODEX PEA 4000116805 to BIRA-IASB; the support of the Czech Science Foundation through project 16-04956S to Charles University, Prague; the support of ESA PRODEX to IAP Prague; the support of CNRS and CNES to IRAP, LPP, LP2CE and LESIA; the support of the German Space Agency through grant 50 00 1603 to CAU; the support of Swedish National Space Board through grants 232/15 and 257/15 to IRF, Uppsala; the support of Academy of Finland through grant 267144 and European Research Council Consolidator through grant 682068-PRESTISSIMO to FMI; the support of ISSI team 'Kinetic Turbulence and Heating in the Solar wind'; the support of FP7 projects STORM and SHOCK. Vlasiator (http://vlasiator.fmi.fi) has been developed with the support of Academy of Finland and European Research Council Starting grant 200141-QuESpace.