The AuCu 3 -type cubic compound, TbIn 3 , undergoes below T N = 32 K a spontaneous magnetic transition at T 1 = 25 K. The magnetic phase diagrams have been determined from the magnetization curves measured on a single crystal in fields up to 10 T. The corresponding magnetic structures have been determined from neutron diffraction studies on the same crystal under magnetic fields up to 5 T. For T 1 < T < T N , the spin arrangement is commensurate, q = (1/2, 1/2, 0), and collinear with the spins pointing along a fourfold axis. At T 1 , the structure remains commensurate, but becomes triple q, with the magnetic moments pointing along the threefold axes. The crystalline electric field (CEF) parameters have been deduced by analysing the magnetic and magnetostrictive properties of the (Tb 0.02 Y 0.98 )In 3 dilute compound, within the CEF susceptibility formalism. Calculations within the mean-field approximation, taking account of CEF, bilinear and quadrupolar interactions, are presented, which describe quantitatively the properties of TbIn 3 in the low-field region.H ex is the exchange molecular field. In the paramagnetic range it is given by:n is the isotropic paramagnetic bilinear exchange parameter. n is proportional to the Fourier transform J (k) of the pair interaction coupling constant J (R j ) at q = 0: