Probability is a branch of mathematics and it is largely used in everyday life. That is why this paper strives to explain the notion of probability and all of its features. The paper will first deal with basic notions and historical definitions of probability which are needed to fully understand this notion. Furthermore, the paper will give an axiomatic definition of probability, point out and prove its features as well as deal with the definition of probability on a discrete probability space and on a set of real numbers. In other words, the paper will observe the problem of geometric probability. One of the ways of setting up probability problems is also the conditional probability, which is of great importance for calculating the probability of an event because it gives us the information if one event had already happened. One can often encounter complex experiments, whose outcome has to be presented using the Cartesian product. That is why the paper will also deal with the notion of probability on a product space. In order to justify the historical statistical approach, the last chapter will introduce the law of large numbers.