Some results in graph theory state: *if a graph G is of fixed order n and has at least size f(n) ( # of edges), then G contains a particular subgraph , or G has some kind of property. *Determining the sharp bounds and resulting extremal graphs is an area of graph theory called extremal graph theory.

We extend some existing extremal results for simple graphs ( *On the extensions of Turan's theorem *) to multigraphs. Also, Ramsey Theory in the context of multigraphs is introduced.