A classification of four‐dimensional Riemann spaces with signature +2 is given. The classification depends upon the differential as well as the algebraic properties of the Riemann tensor. The tool employed is the infinitesimal‐holonomy group of the space. An introduction to the concept of the holonomy group is given, and the technique of classification is outlined. A comparison with the classification of empty spaces given by A. Z. Petrov and with the recent work of E. Newman is also given.