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As we know one of the most important and fundamental books in stability, simplicity, forking and ... classification theory, is Shelah's "Classification Theory" where lots of original ideas of the subject could be found.

I am studying model theory and wanted to start reading that book in order to be able to understand the current literature of the research in the areas of stability and ..., and of course as it is a book that a model theorist must better read.

I ask some of the people around me and they prevent me from reading the book, by the reason that "it is old fashioned and could not enable you to be involved in the current literature of research."

Is this book still recommended or there are some more new resources covering that topics (including the original ideas and the core concepts)?

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I think Shelah's book is very good, but it is very difficult to read, in part intrinsically because of its subject matter, and in part because it was written by Shelah. Recently, Richard Elwes reminded us of the review by Lascar (I do not agree with portions of the review, but it gives you a good idea of what you are up against):

Unfortunately, the book is very difficult to read. This is undoubtedly due in part to the difficulty of the topic itself, but it also has to do with the way the book has been written. The reader should be warned about the numerous misprints and inaccuracies he will have to detect and the time he will need to work out the numerous "easy'' or "left to the reader'' proofs. He will have to understand that statements made under impossibly complicated hypotheses for the sake of generality, and often in an axiomatic setting, may conceal, as a special case, a simple and important fact. Also, he should not expect a rigorous structure: notions are usually introduced when needed, and it will be up to him to guess how important they may be in the rest of the book.

All of these features do not make for easy reading, and we shall certainly not advise anyone (except perhaps the author himself) to "devote himself to reading and solving the exercises till he knows the book by heart'' (cf. Introduction). We do not recommend it as a textbook, and it will be difficult to use it as a reference book, considering how hard it is to find any particular result. But we do think that nobody involved in research in model theory can avoid studying it. We are unable to recommend any particular angle of attack. We did find the opening remarks in each chapter rather helpful (with the exception of Chapter III).

For modern work in the subject, you probably want to read eventually about Geometric Stability Theory, as in Pillay's book. An introduction to stability that would better prepare you for this would probably be best. Pillay's introductory book on Stability Theory is certainly an option. Other suggestions are Marker's book, Poizat's and Hodges's. The truth is, recently there have been quite a few nice texts published, so it should not be difficult to find a good text with which to start.

(But I would still suggest to have Shelah's book as a reference and to consult it as you learn more of the theory.)

On a vein different from the algebraic geometric approach, you may be interested in how set theory interacts with the subject. Shelah's book has plenty of this while constructing non-isomorphic models, but there is significantly more in this direction, in the context of abstract model theory and abstract elementary classes. I would recommend Grossberg's text as an introduction.

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  • $\begingroup$ Thanks for your answer, beside your answer I read Lascar's review and found them very useful. $\endgroup$ – Ali V. Nov 25 '13 at 10:31
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    $\begingroup$ In my opinion the main problem with Shelah's book as a book for a beginner is that one needs to remember that it was written by the originator of a rich and deep theory within few years from creating the theory. Since the time Lascar wrote his excellent review I think that the admiration of Shelah's book just increased. However to recommend that book for a beginner is like suggetsing a begining student of Algebraic geometry to read Grothendick. In my opinion the two best books for beginners (focusing in first order theories) are the books by Chang & Keisler and Tent & Ziegler. $\endgroup$ – Rami Grossberg Mar 9 '15 at 16:15

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