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Designed to be an accessible treatment of the foundations of modern mathematics, the book uniquely bridges introductory mathematics and more advanced topics. The author introduces a variety of mathematical concepts, all of which are typically introduced in logic, foundations, and transitions courses to fulfill general mathematical requirements. Beginning with comprehensive coverage of the necessary building blocks in mathematics, the book quickly explores interesting and provocative treatments of current issues in the field of mathematics and science. While the book can be used as a primer for more advanced mathematical work, the author maintains a useful balance of introductory coverage and mathematical rigor in order to facilitate complete understanding of the presented topics. The book utilizes numerous theorems and proofs to increase comprehension of the concepts, as well as hundreds of completely solved problems at the end of each chapter. The author also includes additional exercises throughout the book for the readers to work through in order to supplement the presented topics. Topical coverage includes: set theory; mathematical logic; proof theory; group theory; theory of functions; and linear algebra.