  We present an exposition on the Fuss--Catalan numbers, which are a
generalization of the well known Catalan numbers. The literature on the subject
is scattered (especially for the case of multiple independent parameters, as
will be explained in the text), with overlapping definitions by different
authors and duplication of proofs. This paper collects the main theorems and
identities, with a consistent notation. Contact is made with the works of
numerous authors, including the early works of Lambert and Euler. We
demonstrate the application of the formalism to solve algebraic equations by
infinite series. Our main result in this context is a new necessary and
sufficient formula for the domain of absolute convergence of the series
solutions of algebraic equations, which corrects and extends previous work in
the field. Some historical material is placed in an Appendix.
