The concept of probability is the Gordian knot of statistics, although the equivalence between the rigorous mathematical definition and the intuitive one (as the ratio of favorable cases to total cases) has some problems. Therefore, we will examine the axiomatic definition of probability and some theorems derived from these axioms. The concepts of sample space and events as well as the operations that can be performed on them are introduced. Some properties of probability are stated without proof, and the important concepts of conditional probability and mutually exclusive events are discussed. To calculate the probability of different events, we introduce the concept of probability distribution, which is fundamental in numerous fields of science, such as statistics and physics, and in their countless applications. This concept and its derived function, the cumulative probability function, are briefly discussed. Finally, the most important probability distribution, which is the Gaussian or normal distribution, is shown as an example.