I’ve read through the rest of Part 1, and it deals mostly with the concept of existence. Specifically he is concerned with concepts of existence, existents, etc., and how these concepts cannot properly capture the existents themselves.
Here’s a stab at a brief description of each chapter. Being brief, it will be slanted toward what struck me as important.
Mythology of Being:
Heidegger presents a mythical history, within which existents are derived from Being.
Ontologization of the Ontical:
This section deals with how the indeterminate is determined as indeterminate. Hegel does something similar making the non-identical, identical. The problem though is that no concept is capable of being nonconceptual. Hegel, being idealist, openly ontologized the ontic, Heidegger conceals the ontologization.
Function of the Concept of the Existent:
Here he talks about the concept of existence, and existentialism in general. Existence is assigned to the individual subject. But this focus on individuality and subjectivity leaves human existence in general, i.e. the essence of humanity, as indeterminate.
Existence Ontological in itself:
Kierkegaard’s way of describing the existence of the individual subject does not differ too much from Heidegger, in its ambiguity and conflation of the ontic and the ontological.
Nominalistic Aspect:
In the relation between the individual subject, and society, nominalism does not provide what is required to place the individual subject as prior to society. Even “my” points to “other”, from which it is distinguished.
Existence Authoritarian:
Here we have explained the problems of subjectivity in general, when existence is assigned to the subject. By excluding what is other, subjectivity produces an authoritarian approach. Rather than being mediated by numerous thinkers authority is attributed to the thinker.
Historicity:
By absorbing “existence”, into “being”, Heidegger allowed the temporal existents to be swallowed up into the eternal Idea. This “historicity” makes historical conditions irrelevant, allowing “history” to be used however one wants. Rather than truth, it’s affirmation.