Claude Levi-Strauss's Mythologiques, of which this is volume 1, are brutally difficult to work through, endlessly fascinating once you get the hang of them, and ultimately not something one ought to imitate or emulate. But until you have read The Raw and the Cooked, at the least, you are not really entitled to speak about the study of myth, and certainly not about structural anthropology (or its weaknesses).The whole book-the whole four volumes, actually-is structured according to a complex musical metaphor, and the Overture to The Raw and the Cooked explicates this metaphor in detail. You'll need to know something about serialism (i.e. Schoenberg) to understand it, but once you do you'll really begin to see what Levi-Strauss is up to. He thinks that myth is not like poetry, and is more like music than ordinary language. I think his comparison is misguided, based on a misunderstanding of serialism, but it's essential to understand why he correlates myth and music to understand the project.
In the main part of the book, he goes on to select a "key myth," a somewhat arbitrarily-chosen tale from the Bororo, a people he has studied fairly intensively (and did some fieldwork among). He then begins a massive project of connecting this myth to other myths from South America, breaking down and analyzing all the little bits and pieces as he goes. The logic can be hard to follow at times; his little diagrams don't help much, and in fact he seems to see this and ditches them in later volumes. But if you lose the thread, you can lose track of the whole book.
Ultimately, he's going to link up a thousand-odd myths from both Americas, demonstrating how each transforms and adds to other themes, until we get a vast complex of American mythical thought laid out in a mesmerizing sort of crystalline web of relations.
In short, Levi-Strauss thinks that myths are a way of thinking, using concrete objects, about such problems as self and other, social relations, kinship, cooking, culture and nature, and so forth. He argues that each myth demonstrates a particular thinking-through of such problems by what amounts to cultures as intellectual entities. This may seem hard to believe, but if you've read The Savage Mind, this is the bricoleur at work.
The big problem, as various people have noted, is that his readings are necessarily somewhat subjective; he could be breaking the myths down incorrectly, splitting up whole units or lumping discrete pieces. What we really see is Levi-Strauss giving it a shot, not a conclusion. Indeed, he calls this a "prolegomenon to a science of mythology," which hits the nail on the head.
I doubt very much whether anyone ought to continue the work, correcting the readings on the basis of further fieldwork or computerized analysis, as he seems to want. Once you've read through this series, you really have to wonder whether it's worth going further, or whether there aren't more interesting questions to ask about mythology. But his point really does stand: myth cannot be taken as a bunch of moral tales and ritual foundations; it must be recognized as thought enacted, or action thought-through.
The big question he doesn't address is history; as in The Savage Mind, he wants to exclude the historical from analysis. Thus the next big step would be someone like Sahlins, who tries to build an appreciation of the historical into structural analysis. Nevertheless, these books really do deserve serious study. If you want to see what mythology really is about "in the raw," as it were, you need to read this. As far as I'm concerned, those who haven't read The Raw and the Cooked have no business saying that structuralism is dead, or that it's unhelpful; they don't know what they're talking about.
Levi-Strauss is a genius, and if he goes in directions that maybe now seem a bit dated, let's remember when he wrote all this stuff (i.e. the 60s). But only the intellectually lazy can afford to pass over this essential moment in the study of myth and religion; we have to work through, not skip over.
