Dixon provides an explicit list of his basic assumptions, which are interesting in their own right. He begins his argument proper with the concept of a "linguistic area", a region within which languages share common features as a result of diffusion. He offers some tentative generalisations about which language features (phonological, lexical, grammatical) are most likely to diffuse, and about the factors that decide which features are borrowed, where they are borrowed from, and who borrows them.
Linguistic areas contrast with family trees, the more familiar classification scheme for languages. Dixon evaluates the criteria for constructing family trees and the ways in which analyses often fail to match the standards set by work on Indo-European. He criticises the proposed Niger-Congo language family, glances at the problems of lexicostatistics and glottochronology, and demolishes the follies of Nostratic and other such super-families. (Here he also explores the consequences of the isolating-agglutinative-fusional cycle for discerning genetic relationships.) The reconstruction of family trees faces problems with proto-languages, with dating, and with the positioning of subgroups.
Turning to modes of language change (and language splitting), Dixon's central thesis is that linguistic areas result from periods of equilibrium, while family trees result from punctuation episodes. Punctuation can be caused by natural events, material innovation, or political and geographical expansion. In general punctuation is associated with aggressive, expanding societies and equilibrium with small-scale ones (a division very much along the lines of Levi-Strauss' hot/cold distinction). This is illustrated with examples from Austronesia, Australia, and the Americas. On less firm territory, Dixon also suggests that the origin of language might be seen as a punctuation event.
Dixon finishes with some applied linguistics. He takes a quick glance at recent history: at invasions and developments in communication technology, and at language loss and the social and political factors that influence it. He goes on to explain why linguistic diversity matters, with a brief tour of linguistic variation around the world, taking adjective classes and the marking of subject and object functions as his examples. Turning to methodological issues within linguistics, Dixon stresses the importance of fieldwork and attacks the myth that purely theoretical work is more difficult and more valuable than description and analysis of languages. He makes a plea for the documentation of languages before it is too late and argues for a focus on "Basic Linguistic Theory" in place of various narrow formalisms.
The Rise and Fall of Languages is an excellent little book, which I warmly recommend to anyone curious about language change. It will be particularly valuable to those in other fields where language change plays a significant part — history, archaeology, and anthropology, among others. Some background in linguistics would be useful (a reference to ergativity on page 18 precedes a not entirely straightforward explanation on page 56, for example), but The Rise and Fall of Languages should be accessible to pretty much anyone. Simple family trees and reconstructions of proto-languages are "sexy", making an effective explanation of their limitations and of alternative models an important antidote to popular enthusiasms.