Introduction: A brief review of elementary number theory; Quadratic domains and ideals: Gaussian integers and sums of two squares; Quadratic domains; Ideals of quadratic domains; Quadratic forms and ideals: Quadratic forms; Correspondence between forms and ideals; Positive definite quadratic forms: Class groups of negative discriminant; Representations by positive definite forms; Class groups of quadratic subdomains; Indefinite quadratic forms: Continued fractions; Class groups of positive discriminant; Representations by indefinite forms; Quadratic recursive sequences: Properties of recursive sequences; Applications of quadratic recursive sequences; Concluding remarks; List of notation; Index.