The textbook 'Number Theory for the External Study of Mathematics' is intended for students of natural science faculties for the discipline 'Number Theory'. The textbook covers the issues of elementary number theory with a focus on divisibility, prime numbers, the principle of inclusion and exclusion, arithmetic functions, Diophantine equations, congruences and number systems. It is specific mainly in that it includes up to 124 model solved problems within the subject areas, which differs from traditional number theory textbooks that mostly contain only collections of unsolved problems within the exercises.