  For the standard Drinfeld-Jimbo quantum group ${\rm U}_q(\mathfrak{g})$
associated with a simple Lie algebra $\mathfrak{g}$, we construct explicit
generators of the centre $Z({\rm U}_q(\mathfrak{g}))$, and determine the
relations satisfied by the generators. For $\mathfrak{g}$ of type $A_n(n\geq
2)$, $D_{2k+1}(k\geq 2)$ or $E_6$, the centre $Z({\rm U}_q(\mathfrak{g}))$ is
isomorphic to a quotient of a polynomial algebra in multiple variables, which
is described in a uniform manner for all cases. For $\mathfrak{g}$ of any other
type, $Z({\rm U}_q(\mathfrak{g}))$ is generated by $n=$rank$(\mathfrak{g})$
algebraically independent elements.
