If we define alienation as the state of being estranged or separated from a group to which one belongs, there are many examples of Meursault's alienation from the society that surrounds him. In the first chapter, he is unable to respond appropriately to the caretaker who offers to take the lid off his mother's casket and questions why Meursault doesn't want to see her one last time. When Meursault watches his mother's friends at the vigil the night before her funeral he acknowledges that he sees them across the room, but he thinks "it was hard for me to believe they really existed." He doesn't overtly grieve the way the others are and is relieved when he can finally escape. 

After his arrest and imprisonment, Meursault's alienation from his society deepens. He is put on trial for the death of the Arab, but his very character is also put on trial as his seeming indifference to his mother's death becomes an issue to the prosecutors. His indifference to his imprisonment and his lack of religious faith are also perplexing to the attorneys, the judge, and the chaplain. His comfort with living outside the expectations of society is seen as evidence of his base character by his persecutors. But since Meursault has chosen his alienation, he is at peace at the end, and he "opened [himself] to the gentle indifference of the world" because he finds it "so much like" himself.  

In the first chapter of The Stranger, Meursault shows no emotion at the news of his mother's death. He is also quite stoic or even casual during the vigil, commenting more on the sights and sounds (i.e. women coughing) than he comments on his own feelings on his mother's death. And when he does comment on these feelings, there is a lack of passion and no feeling of loss. When his mother's friends come to keep vigil with him that night, they seem emotionally affected. Meursault does not. In fact, they sit there in silence and Meursault feels that they are critical of him and his lack of grief.

I inclined to think that they were greeting me, after their fashion, but it had a queer effect, seeing all those old fellows grouped round the keeper, solemnly eying me and dandling their heads from side to side. For a moment I had an absurd impression that they had come to sit in judgment on me.

It is Meursault's cryptic and seemingly uncaring behavior, and others' reaction to him, that gives him this feeling of alienation. When Meursault doesn't react the way so called "normal" people react, those around him are baffled and this compounds his alienation.

After being jailed, Meursault has meetings with the magistrate. The magistrate says it is "unthinkable" that Meursault doesn't believe in God. During these initial meetings, Meursault feels alienated and misunderstood but as the magistrate adjusts to Meursault, he (Meursault) comes to feel "absurdly" like "one of the family.

Finally, Meursault accepts his fate and...