In this thesis, our goal was to define Poisson point processes and introduce some of their basic properties. Firstly, we reviewed the definition of general point processes. Typically, two similar, but different approaches are used for the definition - the first one concentrates directly on the points as subsets of \(\mathbb{R}^d\), while the second approach relies on the concept of random measures. Although we concentrate mainly on the first definition, we point out interesting differences and similarities between those two approaches. After the formal definition of point processes and Poisson point processes, we show some fundamental results from the transformation theory of Poisson processes concerning countable unions of processes (superposition theorem), mapping, thinning and marking. In the last chapter we prove two more substantial results: the Campbell theorem which describes the distribution of the random variable \[\sum_{X \in \varPi}f(X),\] and Rényi's theorem which reveals an interesting characterisation of Poisson point processes using the avoidance function.