  We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with
special emphasis on its the theta function representation of all
algebro-geometric solutions. The basic tools involve hyperelliptic curve
$\mathcal{K}_p$ associated with the Burchnall-Chaundy polynomial, Dubrovin-type
equations for auxiliary divisors and associated trace formulas. With the help
of a foundamental meromorphic function $\phi$, Baker-Akhiezer vector $\Psi$ on
$\mathcal{K}_p$, the complex-valued algebro-geometric solutions of RT hierarchy
are derived.
