  In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it
to describe the Askey-Wilson polynomials. In this paper we introduce a central
extension $\Delta$ of AW, obtained from AW by reinterpreting certain parameters
as central elements in the algebra. We call $\Delta$ the {\it universal
Askey-Wilson algebra}. We give a faithful action of the modular group ${\rm
{PSL}}_2({\mathbb Z})$ on $\Delta$ as a group of automorphisms. We give a
linear basis for $\Delta$. We describe the center of $\Delta$ and the 2-sided
ideal $\Delta[\Delta,\Delta]\Delta$. We discuss how $\Delta$ is related to the
$q$-Onsager algebra.

Rings and Algebras;Quantum Algebra