Probability theory is a rigorous branch of mathematics dedicated to the quantification and analysis of uncertainty and random phenomena. It investigates the likelihood of events occurring, developing axiomatic frameworks, concepts such as sample spaces, random variables, and probability distributions, and theorems to model, analyze, and predict outcomes in non-deterministic situations. This field provides fundamental tools essential for statistical inference, stochastic modeling, risk assessment, and decision-making across diverse scientific, engineering, and economic disciplines.