The main topic of this thesis are Pythagorean triples, i.e., triples of positive integers satisfying the Pythagorean equation. In Section 1 we'll deal with denition and basic conditions of Pythagorean triples. We will show and prove Euclid's theorem for their generalization. At the end of rst section, we'll show that every positive integer is member of some Pythagorean triple. In Section 2 we will present the most important theorems associated with Pythagorean triples. By many examples we'll show connection between Pythagorean triples and perfect squares. We'll test whether areas and sides of Pythagorean triangles are perfect squares. Furthermore, we'll deal with their specic kind, where at least two sides are consecutive positive integers. Finally, we'll explore whether there exist dierent Pythagorean triangles with the same areas. In the last section we'll meet with generalization of Pythagorean triples. We'll describe a way to generate all Pythagorean triples (primitive and non-primitive), and in few examples show how to make them.