It is interesting that if we follow the Neo-Confucian mode of interpretation and read the Classic portion as being by Confucius, then rather than the words of Confucius being treated as commentary on the Five Classics, as the Analects was usually interpreted, we instead get the Five Classics being used as commentary on the words of Confucius. In that sense we can see the structure of the work as marking an important stage in the transition of the image of Confucius from being one of the more eminent practitioners of the scholarly way to being its central figure. The Da Xue may originate, for the most part almost word for word, from the Book of Rites, but as an independent text it is entirely a Neo-Confucian work.
The second portion of the The Great Learning is usually attributed to Master Zeng. It is very plausibly a commentary on the first portion, since it is largely devoted to clarifying the meaning of terms used in the first portion; but it is worth noting that the obvious difference between the two portions is partly due to the editorial work of the Cheng brothers and Zhu Xi, since Zhu Xi remarks that in many cases the tablets were disarranged. One of the things that the Neo-Confucians did was reorder the sections so that the commentary recapitulates the order of the classic on which it is commenting.
We begin, then, with the topics originally mentioned in the classic. Splendid virtue is clarified by identifying three cases in which the notion has been explicitly connected with ancient kings, thus giving the student, if he wished, an idea of where to look if he wants to understand the idea more fully. The next topic is renovation of the people. As we saw, this was a scholarly emendation by the Cheng brothers, which Zhu Xi accepted, and the basis for it seems to have been the fact that the second portion of the text had made a number of references to renovation or newness that, if read as commentary, don't seem to comment on anything in particular unless we take one of the topics to be renovation of the people. From splendid virtue and renovation we move on immediately to the notion of resting in excellence. The fourth chapter, which quotes Confucius on litigation, has a parallel in Analects XII.13, which lets us distinguish sharply between the quotation and gloss. In the Analects, and in old commentary on the passage, it is taken to be clarifying the notion of sincerity, but the Neo-Confucian ordering and interpretation requires us to read it as clarifying the topics of da xue: the root is showing forth splendid virtue and the renovation of the people comes from that.
Perhaps the most interesting chapter of the Da Xue is the fifth chapter of the commentary, on investigation of principle. The Daoxue interpretation and rearrangement of the work is brilliant and makes an immense amount of sense, but when one re-arranges the second portion to conform to the order of the first, you discover (a) that you have a couple of uninformative sentences that don't seem to have a clear place to go and (b) that there is a clear gap in Master Zeng's commentary -- it comments on everything in the classic portion except the investigation of things and completion of knowledge, which are mentioned in the leftover sentences. Given the classic/commentary assumption, then, it is reasonable to conclude that a section is missing. This is precisely what Zhu Xi does conclude, and he makes an attempt to reconstruct its content by summarizing the basic ideas on investigation of principle that arose from the textual and philosophical research of the Cheng brothers. The basic idea of this reconstructed chapter is that the human made is natural disposed to knowing, and everything we encounter in the world has li (principle) that can be known. (We can perhaps think of li here as that in a thing which makes it fit into that greater order in which we also participate by our action.) our potential, therefore, requires that we do not merely stay on the surface of things, but in everything we encounter attempt to reach the underlying li. This is not a short or easy task, but by doing this consistently over a long period of time, our mind will become acute and both world and mind will at some point both be understood.
We then get commentary on the layers of self-cultivation: sincerity, self-rectification, regulation of family, governance of the state, and finally (and extensively) the peace of the kingdom. Thus the overall comment breaks into three parts: three parts on the nature of the Way, one on the unifying subject of the investigation of principle, and six on the working out of the Way in the various aspects or domains of life, which might be held to serve as, respectively, the strategic, operational, and tactical levels of virtuous life.