What makes a conclusion follow from the information we already accept? This textbook approaches that question by connecting the language of logic with the practice of constructing and evaluating arguments. Its introduction presents logic as a foundation of rational inquiry across disciplines, then identifies two central goals: learning first-order logic and understanding logical consequence. The opening sequence develops individual constants, predicates, and atomic sentences before introducing negation, conjunction, disjunction, and conditionals. Readers encounter the distinction between valid and sound arguments, methods for demonstrating nonconsequence, and both informal reasoning and formal proof construction. Dedicated chapters examine proof by cases, contradiction, subproofs, and strategies for using inference rules. The accompanying Fitch software supports the construction of formal proofs, while the acknowledgements explain the package’s connections with Tarski’s World and earlier Hyperproof software. A second major section introduces universal and existential quantifiers, their semantics, and the translation of complex English expressions. Multiple quantifiers, ambiguity, numerical claims, and limitations of first-order expression receive further attention. The final section extends the discussion into set theory, mathematical induction, program correctness, and advanced logical methods. Its concluding topics include the completeness theorem, the Henkin construction, compactness, and Gödel’s incompleteness theorem. Optional sections provide additional routes into technical material, while a glossary, proof-rule summary, and exercise-file index support study and reference.