  In this paper, we study the phase structure and equilibrium state space
geometry of charged topological Gauss-Bonnet black holes in $d$-dimensional
anti-de Sitter spacetime. Several critical points are obtained in the canonical
ensemble, and the critical phenomena and critical exponents near them are
examined. We find that the phase structures and critical phenomena drastically
depend on the cosmological constant $\Lambda$ and dimensionality $d$. The
result also shows that there exists an analogy between the black hole and the
van der Waals liquid gas system. Moreover, we explore the phase transition and
possible property of the microstructure using the state space geometry. It is
found that the Ruppeiner curvature diverges exactly at the points where the
heat capacity at constant charge of the black hole diverges. This black hole is
also found to be a multiple system, i.e., it is similar to the ideal gas of
fermions in some range of the parameters, while to the ideal gas of bosons in
another range.
