The study of groups arose from the theory equations; more specifically form the attempt to find roots of a polynomial in terms of its coefficients, early in the 19th century. The theory of groups itself, which had already been applied in almost all branches of Mathematics, has developed in many different directions. It becomes of prime importance in many Mathematical disciplines.In the present thesis, we have tried to study some points related to solvable groups. We have assumed the group G to be finite group throughout the whole work. In the first chapter, we have pointed out a brief survey of finite groups related to different definitions. We have given statements of some theorems with proofs and some without proofs. In the second chapter, we have discussed solvable groups and some other related definitions. We have also discussed some theorems with proofs and some without proofs. In the third chapter, we have discussed commutators and tried to show some relations of commutators in connection with solvable groups.