The thesis deals with Bayesian approach to statistics and its comparison to frequentist approach. The main aim of the thesis is to compare frequentist and Bayesian approaches to statistics by analyzing statistical inferences, examining the question of subjectivity and objectivity in statistics. Another goal of the thesis is to draw attention to the importance and necessity to teach Bayesian statistics at our University more profound. The thesis includes three chapters. The first chapter presents a Bayesian approach to statistics and its main notions and principles. Statistical inferences are treated in the second chapter. The third chapter deals with comparing Bayesian and frequentist approaches. The final chapter concerns the place of Bayesian approach nowadays in science. Appendix concludes the list of Bayesian textbooks and Bayesian free software.