This manual pertains to the foundational principles of number theory, offering a comprehensive exploration of mathematical concepts. It is designed to cater to a diverse audience, including mathematics majors and students from liberal arts backgrounds, by employing a combinatorial approach. The text covers essential topics such as the basics of number theory, partitions, multiplicativity-divisibility, quadratic congruences, and additivity, providing a robust introduction to the field.

The purpose of this manual is to serve as an educational resource for understanding number theory. It systematically presents key theorems and proofs, enabling readers to develop a strong grasp of the subject matter. The content is structured to facilitate learning and comprehension, making it a valuable tool for students and educators alike seeking to delve into the intricacies of number theory.