Our first main goal was to provide an overview of the theory of Bayesian methods. To do so, we started with probability theory, whose depth and scope are subordinated to the methodological requirements of the Bayesian framework discussed throughout this thesis. We closed that introduction theory with discrete version of Bayes’ theorem which is our cornerstone for following discussion. First step was to lay foundations of Bayesian analysis, emphasizing its practical rather than philosophical aspects. The objective was to employ its framework for combining information derived from different sources – the observed data and prior beliefs. We introduced likelihood functions, prior distributions, posterior distributions, and continuous version of Bayes’ theorem. We next turned to discussing the nature of uninformative and informative priors. Careful selection of the parameters of the prior distributions is necessary to ensure that they accurately reflect our prior intuition. We also presented how to use Bayesian posterior inference to predict realizations of the random variable ahead in time. Bayesian inference is extended with the univariate and multivariate linear regression models. In a normal setting and under conjugate priors, the posterior and predictive results are standard. Our second main goal was to introduce a general framework for reflecting degrees of belief in an asset pricing model when selecting the optimal portfolio. First we discuss the Bayesian approach to mean-variance portfolio selection. The classical framework uses the sample estimates of the mean and the covariance of returns as if they were the true parameters. The failure to account for the parameter uncertainty leads to optimal portfolio weights that are too sensitive to small changes in the inputs of the portfolio optimization problems. Casting the problem in a Bayesian framework helps deal with this sensitivity. Finally, we were combining prior beliefs with asset pricing models to introduce structure and economic justification into Bayesian portfolio selection.