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Based on a series of lectures at Haverford College, Hans Rademacher presents an accessible introduction to number theory, blending analysis and algebra with clarity. Requiring no prior knowledge of the subject, the text covers foundational theorems like prime factorization and quadratic reciprocity, detailed cyclotomy, and Gaussian sums. It previews analytic number theory through asymptotic laws, Dirichlet's theorem on primes in arithmetic progressions, and Brun's twin prime theorem. Rademacher's unique approach integrates analytical methods with arithmetic results, offering both exact identities and asymptotic insights. This classic work remains influential, bridging foundational theory with modern analytical advances, making it ideal for students and enthusiasts alike.