Everything I'm going to say in this review would be picked apart by Levi Strauss because he's very sharp. What I'm saying in this review wouldn't satisfy him or an expert on him so take it all with skepticism. This review is also an unedited mess.
Most of this book is a critique of other philosophers and anthropologists who study totemism. Most of the basis of what Levi Stauss says comes from an iteration of what someone else said. It is important to realize that Levi Strauss wrote this book with an enormous amount data, which he and others collected. Some of the concepts he describes are better understood with charts than with prose. If you want to fully understand what he's trying to convey, understanding the charts is important. Levi Strauss shies away, himself, from defining totemism. Totemism to him, it seems, is not just one thing. He even goes so far as to compare how Yin and Yang is loosely similar to connecting humans to how we conceptualize even the most abstract and metaphysical organizational structures in nature. He even raises how Scandinavians created Loki as a mischievous god and compares him to how a particular animal is seen in another culture. So first and foremost, I think his point is that totemism is a broad range of behavior that allegorically connects humans to animals, and structures human society around these allegories, to different degrees, like with patrilineal and matrilineal societies, prohibitions on diet, and other societal structures. Human interaction and observation, not just on a physical level, with what Levi Strauss calls the spiritual aspect of nature is most important to totemism. To us, the way humans who are very totemic view animals and their spirits is a very complicated and highly structured, multi-step process. That is part of what makes it so hard to define. While he tacitly asserts that everyone is totemic in some way, he mostly exemplifies totemism with cultures in which totemism pervasively occupies most parts of societal structure. There are layers of totemism and each society may or may not have a certain layer, and each layer in each society is different on some level.
Levi Strauss barely touches on why the human mind thinks this way, in the circumstances people who use totemism do. He does not call totemism an old way of thinking. He thinks it's just a way of thinking that people like me do not have. Through other philosophers and anthropologists, he suggests that it's a social, emotional, and evolutionary response to perhaps several human problems. The way totemism's potential purpose in our minds is described is similar to the way people sometimes describe why religion and superstition has a place in our minds. I'd draw criticism for using the words modern to describe why we do not identify ourselves as totemic, because there are people in modern times who still have this practice. I'd draw criticism for using the word civilized to describe those who do not use totemism, because people would think this is offensive to the people he's studying, but he calls them "savage" in another book, and also, it could be argued that modern and civilized people still have some aspects of totemic thought. Levi Strauss still finds a shred of totemism in modern and civilized society. People use semiotics to structure themselves. They find auspices based on symbols they associate themselves with. They change their behavior based on superstition associated with symbols. One, and I think it's the one and only, example he uses is a unit in WWI that called themselves Rainbows. They said "I am a Rainbow" like a savage person would have said "I am a potato." It's like when you compare your friends to animals. "He's like a dog. She's like a cat. Actually she and her friend are both like cats. They are similar." That's totemism at some level. I think totemism is something the occupies the superstitious slot in peoples' brain.
If you want to understand totemism better and receive the full impact of this book, you can research things like an Ogala Sioux Buffalo Dance, or something like that. They even have videos of it from the early 1900's. This book is begging for supplementary exposure to totemism, and not just through other thinkers. It would really help to have some familiarity with things like a few mythical stories from totemic cultures, which Levi Strauss also recants in the book. He also presupposes that the reader has some familiarity with other anthropologists. He does not help the reader much in explaining what other anthropologists thought. This is not a criticism because the book can be read on its own. It's just better with an exploration of its extensive bibliography.
My one huge criticism is that he, or the translator, makes a serious mistake in introducing a term for a particular type of totemism, on a couple of occasions. He uses the term "individual totemism" a few times, and each time, it means something different. He shouldn't introduce a term like this and use it later when it means something very different. It's a problem because each type of totemism is so different to begin with and he makes it seem, at first, like there is a particular category or common form of totemism he's identified, but there isn't. Terminology is very important in this book, but when terms are introduced as being fastened to some form of totemism, and then used more broadly when referring to how totemism takes form in another culture, it's very confusing. This makes a lot of what Levi Strauss says evanescent.
Totemism, and I mean the field and the book, is a terminological nightmare. The word itself comes from an Ojibwa word, so that's already a setback. It has a very specific meaning in that culture and it's been bastardized from the start. How can you expect anthropologists to start assigning terms to aspects of totemism if they can't even agree on what they're looking at? Levi Strauss and other anthropologists often deny the existences of observations of earlier totemic experts.
"The Savage Mind", also by Levi Strauss, was maybe the best non-fiction I've ever read. Totemism was good but not nearly as good as The Savage Mind, which I think encompasses a lot of what he says in this book, and more. Again, this book talks about thinkers ranging from J.J. Rousseau, who had some commentary on totemism, without calling it that, to Radcliffe-Brown. You could even read some of what Immanuel Kant said in "Groundwork of the Metaphysic of Morals" and form your own ideas on what totemism is. Levi Strauss draws from many sources to describe this way of thinking, which, in the end, seems to be too elusive to specifically define. What Levi Strauss has done, is identify it as a societal structure. I am convinced of this after reading The Savage Mind and Totemism.