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I am only superficially familiar with Logic, but I really liked V. N. Bryushinkin's textbook “Practical Course of Logic for Humanities” (Moscow “Novaya Shkola”, 1996): it is written so easily, clearly, with humor and even unexpected examples from the classics (“Winter Notes on Summer Impressions” by Dostoevsky). In general, this is a song:) If only all textbooks were like this!
There are super detailed instructions on this topic, specified in separate sections of logic, from Professor Peter Smith, who taught for a long time at Cambridge. (Smith, Peter. (2015) Teach Yourself Logic 2015: A Study Guide). Available online at the author's website
Here are some decent tutorials that I personally used:
The best of the options I found by the criterion of simplicity (clarity of presentation) and completeness (volume of material covered). On the one hand, the author does not miss a lot of essential details about each topic he examines, on the other hand, he makes the necessary comments quite briefly and clearly. In addition, the book contains basic concepts of fuzzy logic, modal logic, and a lot of non-introductory textbook material.
Smith, Peter. (2010) Introduction to Formal Logic. Cambridge University Press. 3rd printing. – ideal for a leisurely and detailed introduction to the basics of formal logic. Answers to the exercises are available on the author's website. Advantage-gives a very clear and detailed idea of the basics, allowing you to avoid a lot of errors and ambiguities. The disadvantage is modal logic and many other areas of modern logic that are important for analytical philosophy, beyond consideration.
Teller, Paul. A Modern Formal Logic Primer (Prentice Hall 1989). Excellent very detailed and pedagogically talented option for getting acquainted with formal logic. The disadvantage is that after working through both volumes, many areas of logic will remain completely unknown. On the other hand, it is better to lay a good foundation, and not take a lot of topics “on top.” As is sometimes the case in the following version.
Gamut, L. T. F. (1991). Logic, Language, and Meaning, Volume 1: Introduction to Logic. Chicago: University of Chicago Press. Gamut, L.T.F. (1991). Logic, Language, and Meaning, Volume 2: Intensional Logic and Logical Grammar. Chicago: University of Chicago Press. – the textbook is very good for those who are interested in the philosophy of language and related scientific fields, many areas are briefly covered. On the downside , for those new to the humanities who are less interested in the philosophy of language, many sections may be completely uninteresting. From the point of view of consistency and depth of explanation, this option is inferior to Smith and Teller in quality, some distinctions that are essential for the philosophical understanding of logic are ignored, some topics are retold without much reflection on their content. In general, for my taste, for a humanist, there are too many bones of formalisms and too few meat of interpretations.
Sider, Theodore (2010). Logic for Philosophy. Oxford University Press. – the first section of the book is very reactive, the author quickly goes through the basics of logic and this may not be the best first book. But it has very good sections on modal logic in its various variations, two-dimensional semantics, and other topics that are important for analytical philosophy.
Other popular options include
The main problem with this book is the author's completely indigestible style; often very simple ideas are written in such clumsy sentences that even understanding their meaning is difficult to grasp the meaning.