Abstract: The countable random graph, also referred to as the Rado graph, is a very interesting mathematical object as it appears in many different areas of Maths. It can be constructed using ideas from probability and number theory (more precisely the Dirichlet’s Theorem). It possesses nice properties in logic, group theory, the Ramsey theory and topological dynamics. We will touch upon all these areas to see why the Rado graph makes a fascinating structure.