Continued fractions are when you use fractions inside of other fractions. For example, let's say you want to make a fraction like 3/2. But instead of just writing that, you can write it as a continued fraction by writing it as 1 + 1/(1+1/2). That just means the same thing, but the whole number part is shown first, then the fraction part.

Complete quotient,
Methods of computing square roots,
Egyptian fraction,
Engel expansion,
Euler's continued fraction formula,
Infinite compositions of analytic functions,
Iterated binary operation,
Klein polyhedron,
Mathematical constants by continued fraction representation,
Restricted partial quotients,
Stern–Brocot tree,
Śleszyński–Pringsheim theorem