This document provides a comprehensive overview of number theory, covering various topics such as divisibility, greatest common divisors (GCD), least common multiples (LCM), prime numbers, and congruences. It includes detailed explanations, theorems, proofs, and examples related to these concepts. The document also discusses advanced topics like Diophantine equations, continued fractions, and quadratic residues. It serves as a resource for understanding the fundamental principles and applications of number theory in mathematics.