Camus' "The Stranger" begins with a specific death, the death of the narrator, Meursault's, mother:
"Mother died today. Or maybe yesterday, I don't know. I had a telegram from the home: 'Mother passed away. Funeral tomorrow. Yours sincerely.' That doesn't mean anything. It may have happened yesterday."
From this point onward we learn about Meursault and the world he lives in. And as we read, we are at first shocked by what seems to be the cold, uncaring, un-remorseful, and indifferent way that he reacts to his mother's death. It seems that he reacts without reacting. What's going on here? Didn't the man love his mother? How can he be so blah about her death? As matter-of-fact as a telegram?
But, that's the point. It's not that he doesn't care about her death; he doesn't act on or feel anything that he doesn't really feel, and he refuses to act the way others would want him to or expect him to act. He lives in completely honesty with himself and does not act or feel out of any obligation to others. He is true to himself, and that is all that matters to him.
You may not like or approve of a person who is unmoved by his own mother's death, but your judgment is of no meaning or consequence to him. The whole novel is a variation and support of this theme.
To my way of thinking, this reacting without reacting process towards the death of his mother is not related with the point that he loves his mother or not. As he clearly states, death is a part of the life, it will happen one day,how and when it happens is not important to him. He lives with the fact "death" and he acts accordingly. For instance; he killed an arab man and he thinks that this event is not important, and ineffective. He thinks that by hook or by crook he would be death someday by some reason. Moreover, he is sentenced to death through the end of the novel, he again reacts in a careless way towards death, he throws in the towel and becomes ready for death.