Although existentialist themes can be traced all the way back to Socrates and then forward through St. Augustine and Blaise Pascal, to mention only three pre-Kierkegaardian luminaries, Søren Kierkegaard (1813-1855) is rightly regarded as the father of existentialism. His worked proved to be seminal for that of Martin Heidegger, Karl Jaspers, and Jean-Paul Sartre, to mention just three post-Kierkegaardian luminaries. You won't be able to understand properly Angst, Existenz, or Sein-Zum-Tode in Heidegger without having read Kierkegaard. And the same goes for the key concepts of the others who are loosely collectible under the umbrella of existentialism.
Kierkegaard's subjective-existential philosophical approach is one that is the polar opposite of one that could be described as objectivist or cosmological, for want of better labels. Nicolai Hartmann is an excellent representative of the latter tendency. Here is what Wolfgang Stegmueller has to say about Hartmann's attitude toward Kierkegaard (the translation is mine):
In Kierkegaard, the spiritual creator of existential philosophy, Hartmann sees the unhappiest and most cunningly refined (raffiniertesten) self-tormentor of human history. Hartmann denies to anxiety and death any metaphysical significance while admitting their role as emotional phenomena. Only an egotist (Ichmensch) consumed with self-importance sees in anxiety and death something unsettling and terrifying. Cosmically considered, the death of the individual shows itself to be a totally insignificant event in the totality of the world process. It is only an unnatural attitude of protracted self-reflection that artificially induces anxiety of death which then assumes metaphysical weight. (Hauptstroemungen der Gegenwartsphilosophie, Alfred Kroener Verlag, 1960, 242.)
For Hartmann, then, Kierkegaard's concern with the existing individual , and in the first instance himself as existing individual, merely reflects unhealthy self-absorption and egocentricity. The individual, whether an individual rock, plant, animal or man is fleeting, ephemeral, of no final significance.
Maybe I will finish this entry some day. Maybe I will die first. It has been languishing in the queue for many a year. So here it is, a stub. If it gets you reading the luminaries mentioned, then it was worth posting.