Mathematical techniques are developed for studying psychological problems in three fields: (1) psychological scaling, (2) learning and concept formation, and (3) mental measurement. Psychological scaling procedures are demonstrated to be useful in many areas, ranging from sensory discrimination of physical stimuli, such as colors, sounds, etc., through more complex stimuli, such as abstract qualities and concepts, including those involved in job preferences and optimality judgments. Learning and concept formation studies are concerned with the relative effectiveness of different procedures, with developing and testing different theoretical learning formulations, and with the estimation of parameters of learning curves to give more meaningful analyses of learning data. Work in mental measurement is concerned with development of better measurement procedures and with new tests for abilities, such as concept formation and creativity. Several factor analytic studies of mental ability and learning measures establish that abilities are involved in learning tasks that are different from those measured by aptitude and achievement tests.