Main topics of the course include：basic theories about divisibility, primes, congruences, special Diophantine equations, index and primitive roots, quadratic residues and reciprocity, multiplicative arithmetic functions, Dirichlet series, latticen and Minkowski’s theorem, as well as some important applications of number theory. Students are expected to lay down a solid background in number theory, have a feeling of the beauty of the subject, learn about its applications, and get well prepared for subsequent, more advanced courses.