The IPROP Three-Dimensional Beam Propagation Code. IPROP is a nonlinear, three-dimensional, relativistic, electromagnetic particle-in-cell (PIC) beam simulation code written to treat high current electron beam propagation in the atmosphere. As such, it has all the usual features of a plasma simulation code plus air chemistry and particle scattering. The IPROP field solver has been modified to accommodate air conductivity, large aspect ratio spatial zoning, and a moving coordinate mesh. Some specialized diagnostics have been added as well. The field solver, chemistry routine, particle dynamics package, and diagnostics procedures are described in Section II through V, respectively. Here, we comment briefly on the rationale for the particular design chosen for IPROP. At the time that IPROP was written, in early 1983, the few existing nonaxisymmetric propagation codes were limited to simulating the m=1 hose instability in a single transverse plane. Higher azimuthal modes, arising from, for example, filamentation, were not treated. Moreover, the m=1 particle dynamics and air chemistry were linearized. The usual frozen field and paraxial particle motion approximations also were employed.