Doctoral Thesis on Stochastic Learning Automata including Adaptation to Dynamic Markov Environments. The Learning Rules follow the "Bayesian Model" and the thesis successfully demonstrates the effectiveness of Self-Learning Automata. Topics include Stochastic Automata Games, Structured Automata and a short section on hierarchical Learning Automata. These topics are often referred to as Self-Organisation, Machine Learning & Artificial Intelligence. this approach to self-learning is now being applied to topics as diverse as cyber security, adaptive traffic routing, social media advertising and energy grid management. The author - Dr David Eric Probert - completed this thesis whilst at Churchill College & the Statistical :Laboratory at Cambridge University between 1973 to 1976.