The topic of this thesis is the Erdös-Ko-Rado theorem. The thesis is divided into three chapters. In the first chapter, we deal with the basic concepts of intersecting and \(t\)-intersecting \(k\)-set systems and state and prove the EKR theorem. We define and prove some auxiliary statements which are crucial for further understanding. The focus of the next chapter is on alternative proofs of the EKR theorem. The Hilton-Milner theorem is examined, auxiliary statements are defined and the Katona theorem is stated using which the EKR theorem is proved for \(t=1\). At the end of the second chapter, the Kruskal-Katona theorem is stated and it is shown that only canonical intersecting systems meet the bound for \(t=1\) in the EKR theorem. In the final, third chapter, analogs of the EKR theorem are stated. Firstly, Kneser graphs, cliques and cocliques are defined. Later, basic statements are defined and analogs of the EKR theorem are stated for permutations, partitions, vector spaces over finite fields and words.