Rhenium diselenide (ReSe₂) is a layered indirect gap semiconductor for which micromechanical cleavage can produce monolayers consisting of a plane of rhenium atoms with selenium atoms above and below. ReSe₂ is unusual among the transition-metal dichalcogenides in having a low symmetry; it is triclinic, with four formula units per unit cell, and has the bulk space group P1̅. Experimental studies of Raman scattering in monolayer, few-layer, and bulk ReSe₂ show a rich spectrum consisting of up to 16 of the 18 expected lines with good signal strength, pronounced in-plane anisotropy of the intensities, and no evidence of degradation of the sample during typical measurements. No changes in the frequencies of the Raman bands with layer thickness down to one monolayer are observed, but significant changes in relative intensity of the bands allow the determination of crystal orientation and of monolayer regions. Supporting theory includes calculations of the electronic band structure and Brillouin zone center phonon modes of bulk and monolayer ReSe₂ as well as the Raman tensors determining the scattering intensity of each mode. It is found that, as for other transition-metal dichalcogenides, Raman scattering provides a powerful diagnostic tool for studying layer thickness and also layer orientation in few-layer ReSe₂.