This book establishes the basis of a theory of linguistic semantics. The author is very clear with the scope of such a theory: analyzing some aspects of meaning at the level of language as a socio-cultural phenomenon, and not as psychological phenomenon (like in cognitive semantics) nor as a metaphysical relationship between the constituents of signs (like in Pierce's theory). In fact, his focus is on classemes, that is, units of meaning that relate other semantic units together into hierarchies of categories. This allows his method of analyzing meaning to proceed partly from intuition, by relying on the analyst's knowledge of a language and its cultural background.
From that, a structural analysis of a sentence or a text will be the creation of a meta-linguistic model; said model is what is called a structure. This definition of structure is very interesting, as it is a pain point in structuralism to know just what structures are and where they are. Lévy-Strauss famously put them into the head of people; Greimas says they're simply scientific models, which gives them a lot more flexibility and avoids spurious psychological assumptions. Greimas is also very concerned with adding a dynamic aspect to structures, and since they're merely models, it feels almost completely natural to do so. He starts by extracting a very general model of how stories work, called the actantial model, and uses it, in combination with his method, to re-read Propp's theory of folktales and simplify it down to the expression of a broken contract between the hero and other actors, that is repaired or remade anew by the actions of the hero (to summarize very roughly).
To mend together the level of structures and the level of actual words in a sentence, he defines a concept with lasting influence, that of isotopy, that is, the repetition of classemes throughout a text. This is an incredibly powerful concept that gives consistency to and allows precise analysis of how we feel a text is about something and has one or more themes. With this tool, even obscure symbolism can become crystal clear.
Most of the book, if written in a highly abstract and concise style, is actually very didactic and careful. The last two chapters — about which the author warns are more like drafts — are much harder to read, and the overuse of letters to represent words that sometimes aren't even made explicit is mostly to blame. There's a jump in difficulty at that point, and it would have been great if the author had made a much more pedestrian chapter analyzing very closely a short story so that the reader could see how to use the introduced concepts for a full analysis, or even give exercises to the reader like in math textbooks.
Overall, this book is incredible: the tools it gives to its reader are absurdly powerful, especially the analysis of words as classemes organized around a semiotic kernel, the concept of isotopy, the actantial model, and the transformational model extracted from folktales. I've been using them successfully and without too much effort (or rather, I didn't notice those efforts due to the curiosity and excitement to try them out) in the other books I have been reading, and it's made me a much better reader — some texts I appreciate far less due to how ridiculously predictable they become if you apply even basic structural analysis (I've been able to predict almost all of the content of several books only one fourth in), others far more despite their flaws due to how well built their semantic universes are, which I used not to notice this easily.