  In this paper, we study the phase structure and equilibrium state space
geometry of charged topological dilaton black holes in $(n+1)$-dimensional
anti-de Sitter spacetime. By considering the pairs of parameters $(P\sim V)$
and $(Q\sim U)$ as variables, we analyze the phase structure and critical
phenomena of black holes and discuss the relation between the two kinds of
critical phenomena. We find that the phase structures and critical phenomena
drastically depend on the cosmological constant $l$ (or the static electric
charge $Q$ of the black holes), dimensionality $n$ and dilaton field $\Phi $.
