Introduction. Divisibility. Unique Factorization. Applications of Unique Factorization. Congruences. Cryptographic Applications. Polynomial Congruences. Order and Primitive Roots. More Cryptographic Applications. Quadratic Reciprocity. Primality and Factorization. Geometry of Numbers. Arithmetic Functions. Continued Fractions. Gaussian Integers. Algebraic Integers. Analytic Methods. Epilogue: Fermat's Last Theorem. A Supplementary Topics.