Although this is not exactly an introduction to the theory of Existentialism, it is certainly a much more accessible account of it than Sartre's "Being and Nothingness." Sartre addresses the numerous detractors of Existentialism who posit that the theory is essentially pessimistic and anti-humanistic, that it suggests a cynical and amoral view of the world. Sartre argues that man wills what he is (a variant of Heidegger's Being-Becoming), and thus the theory provides for radical freedom. He writes, "when operating on the level of complete authenticity, I have acknowledged that existence precedes essence, and that man is a free being who, under any circumstances, can only ever will his freedom, I have at the same time acknowledged that I must will the freedom of others" (49). Sartre brilliantly links up this conception of radical freedom with the willing of the freedom of others such as communist are Marxist political action. This lecture is a lucid and rich work of philosophy, and it instigated a number of debates around the notion of Humanism, famously refuted by Heidegger.
This collection also includes a Q+A between Sartre and a review of Camus' "The Stranger," which he remarkably compares to Hemingway in terms of prose style. For Sartre, "The Stranger" is the great modern work exploring the fact of absurdity; he indicates that its primary strength is the co-existence of clarity and ambiguity.