Critical Thinking (Richard L. Epstein)

This is a good example of a critical thinking textbook written by someone with a background in mathematics and logic, with a solid familiarity with the philosophical literature on logic and argumentation, who is trying to lay out foundational principles for good argumentative reasoning.

It's designed for classroom use and is one of the best of its type on the market, though it has nothing to say about the psychology of human reasoning or cognitive biases, and nothing to say about argumentation from the perspective of classical rhetoric. I've used this text in some of my classes.

Fundamentally it's not about persuasion per se, but rather the principles of genuinely good rational persuasion. Its focus is applied logic in the broader sense of "principles of good reasoning".

Includes sections on the nature of propositions and arguments, criteria for a good argument, rules for repairing arguments, elements of propositional logic, fallacies, counterarguments, rules for reasoning about analogies, cause and effect, generalizations, evaluating more complex arguments and composing good arguments. Has appendices on using examples in reasoning, truth-tables in propositional logic, Aristotelian logic, and diagramming arguments.

Lots of examples and exercises, and lots of cartoons created specifically for the book.

Epstein has been writing about foundational issues in logic, argumentation and critical thinking for many years, and I've learned a lot from his books. For instructors and people with an interest in a more robust philosophical defense of the definitions and principles he employs in this text, I recommend his book Five Ways of Saying "Therefore", which in many ways is the philosophical companion piece to the textbook.