I would like to begin studying logic on my own. The problem: with the quantity of books available, I have no idea on how to distinguish the good ones from the bad ones. Please suggest to me some good books.
Download the reading Guide on logic books from http://www.logicmatters.net/students/tyl/
§2.2 gives some recommendations for complete beginners.
The rest of the Guide gives extensive advice on further reading.
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Logical Labyrinths by Raymond Smullyan would serve as a friendly introduction to the subject. Smullyan frequently deploys his famous logic puzzles throughout the text to teach a variety of lessons. And a word of warning: friendly doesn't mean easy! Smullyan will push your buttons and make you think deeply about tricky concepts. This one is very rewarding and comes highly recommended.
Read that (pdf) for references. Read C.L. Hamblin's "fallacies", and the stuff by Doug Walton.
Virginia Klenk's Understanding symbolic logic
Hausman's Logic and Philosophy
For a free book, with answers to the exercises online, try Paul Teller's A Modern Formal Logic Primer: http://tellerprimer.ucdavis.edu
For a recent book with similar coverage, and similar virtues of clarity, Logic: The Laws of Truth by Nicholas J. J. Smith (which has got answers to exercises online).
Shorter and even clearer, perhaps, is Peter Smith's An Introduction to Formal Logic (which has also got answers to exercises online). Particularly good on translation in and out of quantified notation which beginners can find a sticking point.
Logic, by Paul Tomassi
I started with logic first by understanding core philosophical concepts, so I would firstly recommend Grayling's Philosophical Logic. That's not a properly answer for your request but is rather a personal recomendation. But if you want to skip the philosophical phase, go and get a Benson Mate's Elementary Logic and than for covering the same issues you have the Smullyan's First Order Logic. Another book that I recommend is Introduction to a Logical-Theory by Peter Strawson, again not covering only formal logic but also philosophical questions that arouse naturally.
Essentials of Symbolic Logic by R.L. Simpson.
I took an Intro to Logic class at school, we used The Logic Book (6th ed.) by Bergmann, Moor, and Nelson. Most of the learning was done out of the textbook; lectures were mainly geared towards asking questions and working through the tougher practice problems. If I recall correctly, the text was fairly pricey but incredibly helpful. The solution manual is online, and I bet you could find the text itself online too with a bit of work. Highly recommend.
Try Nelson Lande's book, Classical Logic and its Rabbit Holes. It's very approachable, even funny. There are solutions to many of the problems online too.
An Introduction to Mathematical Logic (Dover Books on Mathematics) by Richard E. Hodel
Introduction to Logic: and to the Methodology of Deductive Sciences by Alfred Tarski