RbNiF3 is a transparent hexagonal ferrimagnet with Tc=133°K. Below Tc the Ni++ magnetic moments are aligned collinearly in ferromagnetic hexagonal sheets with a stacking sequence of these planes BBABBA such that the A spins are antiparallel to the B spins. This magnetic structure is determined by a 180° antiferromagnetic exchange between nearest-neighbor A, B spins and a 90° ferromagnetic exchange between nearest-neighbor B spins. In this paper we report a detailed inelastic-neutron-scattering study of the spin waves in RbNiF3 both at low temperatures and through Tc. The magnetic unit cell contains six Ni++ spins so that there are in general six distinct branches in the spin-wave spectrum. All six branches are observed in the ΓA direction (c axis), while only the lowest three are observed in the ΓM direction. The measured dispersion curves at 4.2°K may be accurately fitted using simple spin-wave theory with JAB=(93.2±2)°K, JBB=-(21.1±2)°K (H=Σi>jJijS⃗i·S⃗j, S=1), and with all other exchange constants set to zero. Using these exchange constants we can satisfactorily account for other magnetic properties such as the high-temperature susceptibility, the sublattice magnetizations in a field, and two-magnon Raman scattering. At higher temperatures it is found that the c-axis acoustic magnons renormalize like the magnetization, whereas the high-lying optic modes are nearly temperature independent. This leads one to the physical picture in which RbNiF3 at high temperatures is viewed as a set of strongly correlated two-dimensional ferrimagnets composed of three successive planes BAB coupled by the strong exchange field HAB∼6JAB; these BAB "two-dimensional ferrimagnets" are then coupled together by the much weaker exchange field HBB∼JBB.