This work explains the mathematical background of the Black-Litterman portfolio optimization approach. It demonstrates how to achieve more stable portfolio weights in the quantitative selection of securities using Bayesian statistics than would be possible with traditional methods. Chapters 1 and 2 provide an overview of probability theory in general and Bayesian statistics. The third chapter focuses on portfolio optimization, starting with Markowitz's traditional mean-variance approach. Here, the first in a series of examples is presented, serving as a guide for calculations throughout the chapter. After introducing Black-Litterman optimization, the chapter progresses with the step-by-step construction of a BL-optimized portfolio. In the penultimate section of the chapter, various sensitivity analyses of the BL-optimized portfolio weights in response to changes in input parameters are conducted. The conclusion discusses the advantages and disadvantages of the approach.