Existentialism is the philosophy that we are living in a senseless universe without any reason or logic. What happens in this world is therefore incomprehensible and often absurd. Man has no meaning in his life - he is purposeless - except for the simple fact of his existence. In his work The Stranger, Camus conveys this philosophy through the character of Mersault and his experiences, in particular with the death of his mother, his relationship with Marie and his own trial and execution.
When he hears about the death of his mother, Mersault is without emotion, despite the tears and grief of others during the vigil. He appears to be very vague about his mother's life and death, not knowing how old she was. He also is very unsure about when his mother died: "Mamam died today or yesterday maybe. I don't know. I got a telegram from the home. "Mother deceased funeral tomorrow. Faithfully yours." That doesn't mean anything. Maybe it was yesterday." The significant line "that doesn't mean anything" should be read as his reaction to death as a whole, rather than just the truncated form of the telegram.
It is clear that Mersault is indifferent at best to his relationship with Marie, but this is most clearly stated at the end, when he relates:
In the evening, Marie came to pick me up and asked me if I wanted to marry her. I said that it made no difference to me and that we could if she wanted to.She wanted to know if I loved her. I answered as I already had before, that all that meant nothing but that undoubtedly I didn't love her. 'Then why marry me?' she said. I explained to her that marriage was of no importance and that if she wanted, we could get married. Besides, she was the one asking and I was just agreeing to say yes. She then remarked that marriage was a serious thing. 'No' I said. She was quiet for a moment and looked at me in silence. Then she spoke. She simply wanted to know if I would have accepted the same proposal coming from another woman for whom I would have held a similar affection. 'Of course' I said. She then wondered if she loved me. For my part, I could know nothing about it.
For Mersault, with his existentialist perspective, marriage and his relationship to Marie is absolutely meaningless.
Lastly, the unforgettable last lines of the novel express Mersault's desire that "there be a large crowd of spectators the day of [his] execution and that they greet [him] with cries of hate." This final statement reflects the absurdity of life for Mersault and for existentialism - all that can be counted on is birth, and of course, death.
Does Meursault truly espouse existentialism as suggested by the previous answer or is he simply a sociopath without empathy and without remorse for his horrid crime? I advocate for the latter. Meursault, in no personal relationship, exhibited any ability to empathize with any individual. Furthermore, he committed premeditated and calculated murder. His lame excuse that the sun shining in his eyes caused him to commit this act is laughable at face value and is consistent with his dangerous and sociopathic character. Ultimately, the only thing that Meursault found desirous at all in his life was the hope that he would be hated at his demise. This goes beyond absurdity and apathy - he got off on the idea that he would be reviled. To equate Meursault with existentialism, as most do, is to equate existentialists with criminal sociopathy.