Study of Tur?n numbers is a main subfield of extremal combinatorics. Tur?n problems are questions of the following sort. Let F be a family of graphs. How many edges can a graph have if the graph contains no member of F as a subgraph? We will ask this question in the context of hypergraphs. For a graph G, we say a hypergraph H is a G-Berge if each hyperedge h in H can be mapped to two vertices contained in h such that the resulting graph is G. For a graph G, if H contains no G-Berge as a subhypergraph then we say that H is G-free. In this thesis we study the Tur?n number of Berge-hypegraphs. First in the case G is an arbitrary graph and also when G is a complete bipartite graph we study Tur?n problems of Berge-hypergraphs. Then when G is a cycle we evaluate the Berge-hypergraphs in the cases length of G is odd and even
