A concise, systematic introduction to the theory of numbers as understood in ancient Greek mathematics: it defines and classifies integers (odd and even, prime and composite), examines divisibility and factors, treats figurate numbers (triangular, square and other polygonal forms), and explains ratios, means and basic arithmetic operations; throughout the text numerical results are presented alongside the Pythagorean view that numerical relationships underlie harmony and proportion, so the work serves both as a practical handbook for computation and as an exposition of the philosophical significance attributed to numbers.