The work offers a clear, nontechnical exposition of the foundations of mathematics and mathematical logic, aiming to make recent logical results accessible without symbolic formalism. It explains the natural numbers and the definition of number, finitude and induction, order and kinds of relations, similarity of relations, construction of rational, real, and complex numbers, infinite cardinals and ordinals, limits and continuity of series and functions, selection principles and the multiplicative axiom, the axiom of infinity and logical types, general issues in deduction, propositional functions, descriptions, and classes, and concludes with discussion of the relation between mathematics and logic.