Designed for undergraduate students in liberal arts mathematics courses, this text uses puzzles and paradoxes to introduce basic principles of mathematical thought. Decision-making situations that progress from recreational problems to important contemporary applications develop the critical-thinking skills of non-science and non-technical majors. The book covers graphs, logic, probability, voting, and cryptography. It uses a core set of representations, strategies, and algorithms to analyze diverse games, puzzles, and applications. This unified treatment logically connects the topics with a recurring set of solution approaches.