Jean Paul Sartre is often credited with being the father of the existntial philosophical school of thought. However, the title should actually rest with Soren Kierkegaard,a Danish philosopher (1813-1855). He believed that philosophy wasted too much time thinking about the so called realities of the world, or the 'essences'. He felt that nothing could be objective, that all we have in life is subjective truths. For example, the statement 'To kill is wrong' is not always correct, since it is acceptable in times of war etc, so the statement is not objective, it is subjective, becaus eit depends on the circumstances of the time.
So, he argued that what we are, is what we do. We cannot be guided by society, we can only act authentically and be true to ourselves. So we should choose how to act for ourselves, not be driven by society. In this way we can accept resonsibility and make our own choices. This, in essence is actually the foundations of existentialism.
Existentialism, as is evident from the name, is primarily concerned with existence. There are various questions raised by Existentialism like, what is the purpose of my creation? What is the purpose of creation of this universe? Is there any God? Do I have any significance in this universe? Are we free only to be condemned? Etc.
The roots of Existentialism are hard to find. Some critics find it with Jean Paul Sartre because of his renowned book "Being and Nothingness". Some other find its emergence with Schopenhauer who claims, "Existence itself is a crime" and according to him a tragic hero suffers not because of an error of judgement but because of the "Original Sin: the sin of existence". Another set of critics dates it back to the Greeks when Sophocles wrote "Oedipus Rex", stating, "What web has god been weaving for me?"
We can find some glimpses of Existentialism even in Shakespeare, though his writings are not as gloomy as Existentialism is. Hamlet's soliloquy, "To be or not to be that is the question", is all concerned with Existentialism. Similarly, on another place, we find Hamlet commenting upon importance of Man in whole of this cosmology: "…but what a quintessence of dust man is". In the same way, we see Macbeth, saying "where is life?" after the murder of Dunkin. So, we can say that the term Existentialism is probably a production of the twentieth century but the phenomenon is an old one.
Who answered this? "Existentialism" is a term applied in France by the Schools to Heidegger and Kierkegaard as Sartre and Merleau-Ponty emerged during and after the war. It is firstly a term from intellectual history, not hardened philosophical scholarship. As such, it has a broad application. The above answer suggests this. But such application thus may not be rigorous. Kierkegaard is the first to have what might be called the formal concept of existentialism: That the individual human beings relation to being, that is, his (or her) existence, is philosophically primary. A secondary concept which comes from this is that the individual's relation to other passes through this primary relation to being. As being can be said in many ways, so being can be made and experienced in many ways, thus the way one interprets being or questions or interrogates etc. It is what makes one who one is. Obviously this idea can be developed then in many directions and has a certain cache. Hence scholars then go back to find 'origins' of existentialism wherever they find it, but for instance saying it is in Shakespeare is bad thinking: For bits and pieces of a doctrine reformulated retroactively by interpretation do not make the doctrine as such applicable to the figure in question. The whole doctrine has to be there.-Philosophy A.B.D.