I have way too much to say.
Major points:
Existence is absurd.
Existence comes
before essence (we are born before having a real identity or soul).
Choice is very important because our choices determine what our essence is. Within the facticity of existence, what is left to us is our ability to identify situations where we can make choices and then to choose.
The idea of being your own "god" - you are given great power to create your own existence.
Existentialism is ironic, because on one hand we see the absurdity of existing at all, but we place a huge amount of value on ourselves and choices in spite recognizing the absurdity. Kierkegaard takes this to the highest level because he recognizes the absurdity of Christianity (being the most absurd religion, in his eyes) and embraces it because of its absurdity. Despite how I'm making this sound, existentialists aren't crazy, we just see that there is only so much that we know and it leaves us with dilemmas about how to live. Camus says that there is a fundamental question of suicide that we must deal with before we can go on in his "An Absurd Reasoning". If existence is absurd, then why do we live? His answer is that suicide doesn't answer the problem of absurdity. He outlines Sisyphus as the perfect example of someone who recognizes the absurdity of existence and through rebellion and defiance finds meaning (see
my lesson plan on absurdity for more on Sisyphus).
The
Absurdism thread starting at Taliendo's quote defining what the absurd is also good to look at.
The Stranger by Camus is a classic existentialism read that I would suggest as a good starting point.
I could write a lot more, but I'll stop. You might want to get other's perspectives on existentialism, or ask questions because I don't want to hijack this thread as "Will's ultimate take on existentialism and what is good about it and which authors you should read".