A golf putter having a shaft and a putting head connected to the shaft, where the putting head has a first contact surface, a rear wall, a top surface, and a sole. The first contact surface has a concave, partially-spherical face. In a version of the invention, the first contact surface has a first concave, cylindrical face instead of the partially-spherical face. Some versions have a second contact surface opposite the first contact surface. The first contact surface and the second contact surface may have a partially-spherical face, a cylindrical face, or a combination of the two faces. In embodiments with two contact surfaces, the shaft is configured to be reversible such that either contact surface can be used.