Incidentally, I will keep saying Lévi-Strauss "is" this and that, because as I keep reminding people, he's still going. He will be 99 this November. Santé!
When I started putting together a syllabus for a theory of religion course I am teaching next semester, I looked at a bunch of syllabi around for courses like this, and I noticed two things. First, a lot of people won't assign Lévi-Strauss to undergraduates, because he's "too hard." What that really means is that he's too hard for the teacher, not for the students. He's hard, yes, but on the other hand he writes very, very clearly, so if the teacher understands the material it can be taught. The students won't master the text, but then again they're not going to master Durkheim either, and people teach him. Same with Turner, Geertz, and the like. I notice that a lot of teachers also get cute: they say, "no, Lévi-Strauss has nothing to do with your favorite jeans, ha ha." Yeah, well, actually Lévi-Strauss says the jeans guy is a distant cousin, so let's not get too clever.
The other thing I noticed is that when people do assign Lévi-Strauss, they usually assign Structural Anthropology, which strikes me as idiotic. I tried it once -- anyone can be a fool once -- but to keep doing it? Didn't they learn from their mistakes?
So I thought it might be helpful to walk through a kind of course of reading. Nobody is likely to do all of this; that's not the point. The point is to take it as far as you want to, for your purposes, and track his thinking and your interests as you go, so that you get the most out of whatever you do intend to read. Here goes.
The first thing is to read Tristes Tropiques. Assuming you are reading in English, use the Weightman translation which is complete and excellent. What you should get out of this is an understanding of who Lévi-Strauss is, how he thinks, what he did ethnographically, and the like. You should, if you are reading with attention, come out mesmerized by Lévi-Strauss, whether you agree with or like him or otherwise. He is frighteningly intelligent, one of the true geniuses of the 20th century, and this book is a prose masterpiece. For those of you who know what this means, the book essentially would have won the Prix Goncourt, except that it is not fiction; they actually announced their regret, which is extraordinary. So read it as a novel and a meditation. Let yourself be swept away. Hold your critical comments until a second reading, if possible. Bear in mind also that anthropological field methods have changed pretty drastically since the 1930s, so some of the things he did and thought appropriate will shock you if you know much about ethnography today.
Okay, now you're ready. You know what he's like, and you've got some idea how he thinks, but how does he really think?
So now you read The Savage Mind, or better yet La pensée sauvage. The translation is execrable -- really irresponsible and just plain bad, with technical terms translated indifferently, sentences mysteriously dropped, and the like. Nevertheless the content is sufficiently powerful that it comes through anyway, mostly. If you are not very, very up on Sartre, you will not get much out of the final chapter, but that's okay.
As you read, try to work through the examples as much as you can. Bear in mind that Lévi-Strauss will often propose analogies that seem nightmarishly difficult, making things worse than ever. In a number of cases, however, that is because of a difference between your education and his. Specifically, when he went to school, every French kid was supposed to know about people like the painters Clouet and Poussin, and all educated people were supposed to have a clue about music as well, and so on. So he will propose analogies to this sort of material -- essentially classic European high artistic culture -- and if you don't know what he's referring to it can indeed make things worse. Note also that the same effect happens with bricolage, that most famous of analogies. Everybody in France knows what bricolage is, because it's a normal word from everyday life. Lévi-Strauss's particular usage is a little old-fashioned, but not much so; certainly any French reader would know just what he has in mind quite quickly. American readers don't have this reaction and get lost just when he's trying very hard to make it simple.
Anyway, work through this book slowly and carefully. He moves very fast, and you can lose the thread if you're not careful. If you do get lost, stop and back up. In many books, you can just plow on a paragraph or two and you'll pick it up again, but this is often not the case with Lévi-Strauss, particularly in La pensée sauvage.
At this point you are ready to follow a path of thought. To my mind, the ones that are most likely to be useful or interesting to follow are myth, structural analysis as a method, and art. You could go other routes, but I think picking one of these is probably most helpful.
If you want to follow Lévi-Strauss on myth, start with Myth and Meaning, which is interesting without being especially concrete about anything. Then The Jealous Potter, which is great fun, and then The Story of Lynx. If you still want to continue, now that you have some idea what you're getting into, start in on Mythologiques with volume 1, The Raw and the Cooked. The other volumes are From Honey to Ashes [seems to be out of print, which is odd], The Origin of Table Manners, and The Naked Man. If you actually get through all this with any idea of what's going on, you can count yourself among the very, very few.
At that point, you might turn to Structural Anthropology and read "The Structural Study of Myth" and to Structural Anthropology 2 for "The Story of Asdiwal." But these things will now read as preliminaries, which they are. I don't recommend reading them first because he changed his mind so much during the Mythologiques project. If you look at remarks on Lévi-Strauss's study of myth, you will often see these articles referred to and not Mythologiques. Well, if you do that, you don't really know what you're talking about, unless you have some good and stated reason for dealing only with his early thinking on the issue.
Backing up, Myth and Meaning is easy, by Lévi-Straussian standards, and The Jealous Potter is not difficult. The Story of Lynx is a bit trickier, but not bad at all. But The Raw and the Cooked is I think the most difficult book I have ever read. It is more difficult, for example, than the rest of Mythologiques, because by the time you get to volume 2 you have some idea what he's doing and how, which you had to figure out in volume 1. It is more difficult than any of the Derrida I have read: Derrida is often difficult because his language is so weird and idiosyncratic, and his ideas are very strange, but ultimately once you get the hang of it he's really just difficult. The Raw and the Cooked is lie another order of magnitude. I am convinced that a very large reason why so many people so happily accepted the pronouncements that Structuralism was dead, particularly in anthropology, was because it meant they didn't have to get through this book.
But it's really worth it. It's absolutely fascinating. By the end of the four volumes, you will feel like your brain has been blenderized, but in fact once it settles a bit you will actually think quite differently about a lot of things, and certainly you will think rather more clearly about a lot of things, whether you like it or not.
At this point, if you want to continue, I'd suggest going to methodology, but art would make sense as well.
Structural Analysis As Method
Here you will need to work more or less in chronological order, because you need to see how Lévi-Strauss's thinking has developed. Start with Introduction to the Work of Marcel Mauss, and if you haven't read Mauss's The Gift and A General Theory of Magic you may want to check those out as well, though it's not entirely necessary; reading Mauss's Sacrifice wouldn't hurt either. Properly speaking, Mauss co-wrote mostly with Henri Hubert, who should get a fair bit of credit, but Mauss always gets top billing.
Next read Structural Anthropology and Structural Anthropology 2, and then The View From Afar. Because these are all essays, they are digestible, and they cover the range of his interests pretty well. Now that you know what you're getting into, read The Elementary Structures of Kinship, which is foundational for his methodology.
Now go back and re-read La pensée sauvage, which will look rather different this time around. If you still want to continue, jump over to the myth track and go on from there.
Personally, I think this approach is the least rewarding way to read Lévi-Strauss, because it is quite dry and you never quite get a full sense of what he has in mind. But some people like this stuff all by itself, in which case, good for you, I guess.
This is a good deal trickier to run through directly, because there are essays and bits scattered all over the place. The only thing I know of that is absolutely central here, apart from all those discussions in La pensée sauvage, is Look, Listen, Read, which is mysteriously out of print; it was just reprinted a few years ago in paperback, so there are copies around.
Assuming you want to continue, I think probably you should read the introduction ("Overture") to The Raw and the Cooked, and the "Finale" to The Naked Man, and then there is some good material in The View From Afar and Myth and Meaning. Much of this is about music, you should know in advance. There are passing discussions elsewhere, in fact throughout his monumental oeuvre, but these would be the obvious "go-to" texts. Once you've read Look, Listen, Read, you'll have some idea where he's going and what he will connect up to the arts.
There are other texts, but not too many. Certainly if you've gotten through some large block of this material, you don't need my guidance, and if you've sat down and read straight through from myth to method to art, you should probably be teaching this stuff instead of me.
I will just mention a few things about secondary sources, in list form:
Marcel Hénaff's Claude Lévi-Strauss and the Making of Structural Anthropology is I think the best book overall, but it is rather dense -- as it should be, really.
Jacques Derrida's essay "Structure, Sign and Play in the Discourse of the Human Sciences" (in Writing and Difference) is excellent and amazingly important, but you have to have read quite a lot of Lévi-Strauss in advance. Same goes for the brilliant discussion of "A Writing Lesson" (a chapter in Tristes Tropiques) in Of Grammatology.
Edmund Leach's Claude Lévi-Strauss is useful in its way, and short, but (a) it doesn't take us very far into his career, and (b) it is markedly hostile on a lot of counts, so it has to be taken with a grain of salt.
David Pace's Claude Lévi-Strauss: The Bearer of Ashes (out of print) I did not find especially useful, although there are some interesting gems and it is fairly approachable on the whole.
I haven't seen a lot else that is especially helpful for understanding Lévi-Strauss. Obviously there are interesting discussions and the like, but as things to help you read Lévi-Strauss, these are so far as I know the best. In the end, Lévi-Strauss is a better writer than any of these people, and he says what he means rather better than they do. So you want Hénaff because he covers everything and can help you when you get stuck, and you want Derrida because he turns Lévi-Strauss inside-out and does brilliant things with him. Myself, I don't want Leach or Pace as intros, because I think they're not helpful; I mention them only because they come up a lot when people go looking.
So that's my introduction to how to read Lévi-Strauss. Now get cracking, people -- you've got your summer reading list all set, so take a stack of Lévi-Strauss to the beach!