§ 1. Continued fractions and their convergents § 2. Representation of irrational numbers by continued fractions § 3. Law of best approximation § 4. Continued fractions of quadratic irrationals § 5. Application of the continued fraction for √D in solving equations $x^2-Dy^2$ and $x^2-Dy^2=-1$ § 6. Continued fractions other than simple continued fractions