Camus's book 'The myth of Sisyphus ' draws our attention to the word “absurd”. Attributed to Camus, absurd and thus considered to be a new modern philosophical thought. But what is the meaning of the absurd in philosophical terms and how it differs in the meaning of everyday language. In this paper, we first traced the history of this absurd philosophy with the influence of nihilism, and then through the study of the myth of Sisyphus, analyzes the new connotation of the word absurd given by Camus and attempted to explore the various contradictions of absurd philosophy. Another study of this paper focuses on analysis of Camus's dramatic work 'Caligula'. In addition to explaining why did Camus choose the legendary tyrant as the embodiment of his absurd philosophy, it is also necessary to clarify the darkness or the meaning of the absurd in this play. The analysis in this section will point out the correspondence between Caligula and the philosophical writing about the absurd. This study aims to present how Camus express the philosophy of the absurd through drama, but the more important research topic is to explore the difference between this absurd philosophical theory and its dramatic practice.