TRISTAN-MP is a fully relativistic Particle-In-Cell (PIC) code for plasma physics computations and self-consistently solves the full set of Maxwell’s equations, along with the relativistic equations of motion for the charged particles. Fields are discretized on a finite 3D or 2D mesh, the computational grid; the code then uses time-centered and space-centered finite difference schemes to advance the equations in time via the Lorentz force equation, and to calculate spatial derivatives, so that the algorithm is second order accurate in space and time. The charges and currents derived from the particles' velocities and positions are then used as source terms to re-calculate the electromagnetic fields. TRISTAN-MP is based on the original TRISTAN code (ascl:2008.025) by O. Buneman (1993).