While Confucius is mentioned and quoted in passing in this book, this book consists entirely of comments by, and anecdotes about, some of his students, and in fact divides very clearly into a section for each student. The students we get are:
Zhuansun Shi (Zizhang): He notes that a public official should focus on the task at hand (19.1) and insists that virtue requires constancy (19.2). He takes a more moderate view than Zixia on how the noble should relate to others, arguing that the noble person should not reject the masses but tolerate them (19.3).
Bu Shang (Zixia): He holds that all arts have something of value in them, but they are not all equally valuable to the noble, who will avoid getting bogged down in the lesser ones (19.4), and suggests that fondness for learning is associated with recognizing one's limitations but remembering one's potential (19.5). When criticized by Ziyou for his students' attention to external details, he responds that only the truly wise can grasp things all at once; everyone else must start with elementary matters (19.12).
Yan Yan (Ziyou): He has two cryptic comments, one on the nature of mourning (19.14), and one on the nature of Zizhang (19.15).
Master Zeng: We have met Master Zeng before. He also comments on Zizhang (19.16) and gives the two quotations from Confucius that are found in Book XIX (19.17, 19.18), both on filial piety.
Duanmu Ci (Zigong): Most of his comments are defenses of Confucius. When asked who was Confucius's teacher, he replies that the Way (Tao) of the great kings, Wen and Wu, is still present and within us; thus Master Kong learns from everyone, without having to have a regular teacher (19.22). When someone says that he is even better than Confucius, he compares this to a wall around a house: his wall is short enough that ordinary people can see over it to admire the house, but Confucius's wall is so tall that only those who can find the gate can see how splendid his palace is (19.23). Master Kong is as far beyond others as sun and moon (19.24) or Heaven itself (19.25).
All of these students were known in later times as founders of important earlier Confucian schools, so one suspects that part of the point of this chapter is precisely to display Confucian thought as diversified, yet unified, in the different schools that arose from Master Kong's teaching.
The final book of the Lun yu appears to consist just of fragments, perhaps as a sort of appendix. We have what seem to be excerpts from a lost document (20.1), and then a long discussion between Zizhang and Master Kong about the five excellences and four abominations in governing (20.2). All of the excellences are forms of moderation, and the four abominations are to put people to death without first educating them, excepting tasks to be done without giving forewarning, insisting that others meet one's own time frames while not caring about theirs, and being stingy rather than generous. And the last analect (20.3) serves nicely as a summary of the key ideas of the entire book, so I quote it in full:
The Master said: 'If one does not understand fate, one has no means of becoming a gentleman; if one does not understand the rites, one has no means of taking one's stand; if one does not understand words, one has no means of understanding people.'
Quotations are from Confucius, The Analects, Raymond Dawson, tr., Oxford University Press (New York: 2008).