  In this article, we define and study the affine and cyclotomic Yokonuma-Hecke
algebras. These algebras generalise at the same time the Ariki-Koike and affine
Hecke algebras and the Yokonuma-Hecke algebras. We study the representation
theory of these algebras and construct several bases for them. We then show how
we can define Markov traces on them, which we in turn use to construct
invariants for framed and classical knots in the solid torus. Finally, we study
the Markov trace with zero parameters on the cyclotomic Yokonuma-Hecke algebras
and determine the Schur elements with respect to that trace.

Representation Theory;Geometric Topology;Quantum Algebra