A new model of random graphs with preferential attachment has been newly introduced by Albert and Barabasi to explain better the phenomenon of real-world networks, e.g., the web. In this talk, I will first introduce the basic notions of a graph theory. Then I will give some examples of random graph models: Erdos-Renyi model, Gilbert model. Finally, I will discuss the model introduced by Albert and Barabasi and the recent results on the degree sequence of a scale free random graph process.