We have carried out multireference configuration interaction calculations with a large basis set for the H2Br system at 104 geometries preselected for convenient use in fitting an analytic potential energy surface for the reactions H + HBr --> H2Br and H + H’Br --> H’ + HBr. The external part df the correlation energy is scaled (SEC method) to yield a 101 geometry data set which is fitted using the extended London-Eyring-Polanyi-Sato method with bond-distance- and internal-angle-dependent Sato parameters plus a three-center term localized at the collinear H-Br-H saddle point. The unweighted root-mean-square error for 88 points corresponding to collinear and bent H-H-Br geometries and collinear H-Br-H geometries is 0.55 kcal/mol, with larger deviations for bent H-Br-H geometries. Rate constants were calculated by combining the new analytic potential energy surface with improved canonical variational transition state theory and the least-action semiclassical tunneling approximation. : For the abstraction reaction, H + HBr --> H-2 + Br, and four deuterium and muonium isotopic analogs, agreement with experiment is very good; however, it would probably be better if the 1.9 kcal/mol classical barrier height on the analytic potential energy surface were lowered by 0.15-0.6 kcal/mol. In contrast to die previous interpretation of the experimental results for Mu + HBr, our calculations show that the Mu + HBr reaction is dominated by tunneling at all temperatures for which it was studied experimentally, up to 479 K. Tunneling is also found to be important for H + HBr and H + DBr, increasing the predicted rates at 300 K by factors of 2.6 and 1.8, respectively, whereas the same factor is only 1.4 for both D + HBr acid D + DBr. Agreement with experiment is much less satisfactory for the exchange reactions D + KBr reversible arrow DBr + H; the present barrier height of 12 kcal/mol would have to be lowered about 7-9 kcal/mol to improve this situation. The assumption that high-frequency vibrations remain adiabatic prior to the region of large reaction path curvature predicts that vibrational excitation increases the reaction rate by factors of 1600-19 000 at 600 K, in qualitative agreement with the experimental factors of 3100-37 000.