Logic: The Laws of Truth (Nicholas Smith)

This 2012 text is very good.

The book is intended as a first full course in first-order logic with identity that covers enough information so that students can transition naturally into studying a wide range of specialty topics, including

• nonclassical logics (modal logic, tense logic, relevance logic, many-valued logic, fuzzy logic, etc.)
• mathematical logic (more advanced metatheory, e.g. Lowenheim-Skolem and compactness theorems, undecidability of first-order logic, Godel's incompleteness theorems, etc.)
• theory of computation (e.g. models of computation, Turing machines, register machines, computable and uncomputable functions, etc.)
• philosophical logic (e.g. monism vs pluralism, normativity of logic, logic and reasoning, logic and ordinary language, theories of truth, etc.)
• set theory (e.g. axiomatic set theories, consistency and independence, foundations of mathematics, etc.)
• formal semantics (e.g. generalized quantifiers, theory of types, categorical grammar, intensional semantics, Montague grammar, etc.

Just to be clear, this text doesn't cover all of these topics. What it does is provide the student enough preparation to be able to move on to these topics, if they so wish.

This is the primary goal of the text, and I agree with the author that it fills a gap in the available textbook offerings. Many students complain that the jump from their first introductory logic class to more intermediate and advanced topics is so great that they struggle to get their bearings. This text is designed to ease that transition, and I think it does a good job of it.