This book is an outstanding introduction to logic and numerous other discrete mathematical topics (e.g., induction, set theory, recurrence relations, a bit of modern algebra, graph theory, and more). Nominally aimed at introductory computer science and mathematics students, it is also an excellent reference for more advanced readers. I am by no means a professional mathematician, but am also well beyond being an introductory student -- and I learned a great deal from this book, and still refer to it.
The unique feature of A Logical Approach to Discrete Math is its presentation of logic via an equational calculus: The book treats logic as a set of rules under which certain symbolic expressions are equivalent to others, with little or no concern for the meaning of those expressions. Even such elements as "true" and "false" are largely symbols related to one another by rules, not names for intuitively understood concepts. This view of mathematics is radically different from what many computer scientists were trained in, or train our students in. Studying it opens whole new perspectives on the power of mathematics, and new ways of thinking about it (an intellectual system that can abstract all meaning away from its subjects of study, and still achieve useful, even deeply insightful, results about those subjects, is awe-inspiring).
While A Logical Approach to Discrete Math is a very good book, I do find myself wondering if it is appropriate for all introductory students. Many people say they have successfully taught such students from it, and I have not taught a course based on it myself. But I do find that my introductory computer science students often seem to reject mathematical thinking because they understand it only as manipulation of inscrutable expressions by cryptic rules, with no underlying intuition. They desperately need to understand that those expressions capture a meaning, and that the rules are designed to preserve the meaning while changing its form. A Logical Approach to Discrete Math does not meet this need well.
Despite this concern, A Logical Approach to Discrete Math is a wonderful book, with which every computer scientist and mathematician should be familiar. It contains powerful wisdom -- which is a great strength, but also means it should be given to novices with care.