Culver's introduction to his section on legal positivism is mainly devoted to Hart. The first part of the introduction (through section 1, pp. 89-91) is relevant to this first assignment from Hart.
Although Hart addresses the topic suggested by the title throughout this paper, the heart of that discussion is in the second half. In the first half, after introducing (in section I, pp. 116-122) the views of Austin (and Bentham) on the subject, Hart considers several criticisms of Austin, accepting some parts of these criticisms and defending Austin against others. His aim in each case is to show that these criticisms concern issues that are independent of Austin's claim that law and morality are separate. But the issues that Hart thinks are really at stake in these criticisms are important for his own theory of the law, and his discussion of Austin here also amounts to an introduction to Hart's theory (which we will encounter in the selections from his book The Concept of Law).
In section II, Hart looks critically at Austin's way of describing law as the command of the sovereign. He focuses on two points, Austin's characterization of the sovereign in terms of habitual obedience (see p. 124) and his insistence that laws are a kind of command (see pp. 125-126). These are the core of Austin's view of the law, and the alternative views regarding these issues that we will later see in the selections from Hart's book are at the core of his own theory of the law.
Section III (pp. 126-134) is directed at the Legal Realists, and represents a substantial part of Hart's response to their "rule skepticism." The idea of "problems of the penumbra" (p. 127 c. 2) is the key one here. Think about it and the example Hart uses to present it. Towards the end of this section, Hart alludes to certain Nazi statutes; they are to tied to an issue that Hart will discuss explicitly and at length in the second half of the paper (and that is addressed also in the hypothetical case due to Lon Fuller that you will read along with it for Monday).