2012 Reprint of 1955 Edition. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. A stochastic process is one in which the probabilities of a set of events keep changing with time. Bush and Mosteller make use of the mathematical techniques developed for the study of such processes in building a theory of learning and then apply the theory to explain the results of several learning experiments. Contents: Part I: The mathematical system and the general model – 1. The basic model – 2. Stimulus sampling and conditioning – 3. Sequences of events – 4. Distributions of response probabilities – 5. The equal alpha condition – 6. Approximate methods – 7. Operators with limits zero and unity – 8. Commuting operators – Part II: Applications – 9. Identification and estimation – 10. Free-recall verbal learning – 11. Avoidance training – 12. An experiment on imitation – 13. Symmetric choice problems – 14. Runway experiments – 15. Evaluations.