Credibility theory is statistical inference used to make prediction based on both individual risk data and collective risk data. It is widely used in the insurance industry to predict the future claim payment, determine the insurance premium and determine the size of required reserve. This course will provide a mathematical treatment on credibility theory and explore the application of the theory in prediction of future claim payment, premium calculation. Topics include limited fluctuation credibility theory, greatest accuracy credibility theory, credibility premium, Buhlmann models, Buhlmann-Straub models and applications of credibility theory in solving insurance problems such as future loss prediction, premium calculation etc.