In this nal work, we are studying the modal logic that emerges as a result of classical logic. We are not interested anymore in statement like 'A is true' but statements like 'A is possible' or 'A is necessary'. Through reading this nal work, the Reader will be introduced with the development of modal logic throughout history and with basic terms such as K modal system and Kripke's frame. We will advert examples, proofs and interpretations of some equivalent statements. In the third chapter we will get acquainted with the semantics of possible worlds and prove the main theories of modal logic, such as the soundness theorem and the completeness theorem .