Existential phenomenology is Martin Heidegger's brand of phenomenology.
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Overview
In contrast with his former mentor Edmund Husserl, Heidegger (in his Being and Time) put ontology before epistemology and thought that phenomenology would have to be based on an observation and analysis of Dasein ("being-there"), human being, investigating the fundamental ontology of the Lebenswelt (lifeworld, Husserl's term) underlying all so-called regional ontologies of the special sciences. In Heidegger’s philosophy man is thrown into the world in a given situation, but he is also a project towards the future, possibility, freedom, wait, hope, anguish. In contrast with the philosopher Kierkegaard, Heidegger wanted to explore the problem of Dasein existentially (existenzial), rather than existentielly (existenziell) because Heidegger argued Kierkegaard had already described the latter with "penetrating fashion".
Development of existential phenomenology
Besides Heidegger, other existential phenomenologists were Hannah Arendt, Karl Jaspers, Emmanuel Levinas, Gabriel Marcel, Jean-Paul Sartre, Simone de Beauvoir, Maurice Merleau-Ponty, Enzo Paci and Samuel Todes.
Other disciplines
Existential phenomenology extends also to other disciplines. For example, Leo Steinberg's essay "The Philosophical Brothel" describes Picasso's Les Demoiselles d'Avignon in a perspective that is existential-phenomenological.