The distribution of incurred losses for insured events and the subject of Credibility Theory are the main objectives to be delivered.  Loss Distributions include; Construction of Empirical Models,  Construction and Selection of Parametric Models, Interpolation and Smoothing ,Simulation. In the Credibility Theory: limited fluctuation credibility, Bayesian credibility: non-parametric and semi-parametric, Bühlmann and Bühlmann-Straub models, Conjugate priors will be covered.