When philosophers do ontology (coming up with a list of types of things that "exist," what are they actually doing? Martin Heidegger thinks this is a real problem: What is existence? What is "being?" It is, he thinks, the core problem behind all of philosophy, the underlying thought nagging us that needs to be settled before we can ground science coherently discuss ethics or anything else. Worse yet, though we start our inquiry with some intuitive notion that there is a problem here, this doesn't come to us formulated in a specific, concrete question, so we not only have to answer the question; we have to figure out what the question is.
Heidegger's answer, not surprising given that he was Husserl's student, is that we need to use phenomenology, i.e. the careful description of experience, though Heidegger has different ideas than Husserl about exactly how this can be most fruitfully done. So to figure out being, we end up by starting with an analysis of "the being for whom being is a question," i.e. ourselves.
We'll be reading the beginning of Heidegger's most famous work Being and Time (1927): definitely the Introduction and Chapters I and II of Part One, though our discussion may range through Chapter IV.