Ramsey theory is one of the branches of mathematics that starting in 1930 with Ramsey . There are many interesting applications of ramsey theory in other branches of mathematics such as number theory , logic , analysis , algebra, geometry and information theory . The Ramsey number r(m,n) , is the smallest N such that in every two – coloring of the edges of graph K N using colors red and blue, either the blue subgraph contains an m – element independent set or the red subgraph contains an n – element independent set. Many generalizations of Ramsey number have been gotten yet. In this thesis we are studing some types of these generalization Ramsey number, such as Irredundant Ramsey number , upper domination Ramsey number , mixed domination Ramsey number, mixed Ramsey number, bipartite rainbow Ramsey number, induced Ramsey number, weak induced Ramsey number, induced planar Ramsey number and weak induced planar Ramsey number.