In this part of the lecture, Kripke addresses the issues you have encountered in the two papers by Quine.
• First he discusses the ideas of the necessary, the a priori, and the analytic (pp. 34-39). Kripke begins with a discussion of the logical complexity of the concept of the a priori (pp. 34-35) and ends with a suggested account of the meaning of "analytic" (p. 39). However, the material in between is the most original; there he distinguishes between the a priori and the necessary in a way that points to the possibility of necessary truths known a posteriori and contingent truths known a priori. Although his discussion of the Goldbach conjecture points to an example of the former, clearer and more important examples will appear later. The idea of the contingent a priori is less central to his later discussion, but he will offer an example in the final part of the first lecture and another sort of example later in the book.
• Next comes a discussion of issues concerning necessity, reference, and quantification--in particular, the idea of necessity de re--i.e., the idea of properties that hold necessarily of things independently of the way they are referred to. First he outlines Quine's concerns about quantification and modality (pp. 39-42). Then he restates the issues as a problem of "transworld identification" (pp. 42-43). Next he argues that this is a pseudo-problem (pp. 43-47). In the assignment for Friday, he present his own view of necessity de re.