  We provide a unified description of thermal equilibria of black hole
accretion disks, including the newly-discovered advection-dominated solutions.
We classify the solutions on the basis of optical depth and importance of
advection cooling. We demonstrate that only four physically distinct
topological types of equilibria exist. Two of the types correspond to optically
thin and optically thick equilibria, while the other two types are
distinguished by whether advection is negligible or dominant. A stable
Shakura-Sunyaev disk exists only for accretion rates $\dot M$ below a certain
maximum. However, there is a critical viscosity parameter $\alpha_{\rm crit}$,
which is a function of radius, such that for $\alpha>\alpha_{\rm crit}$
advection-dominated solutions exist for all $\dot M$. Even when $\alpha<
\alpha_{\rm crit}$, the advection-dominated solutions are available for a wide
range of $\dot M$ except for a gap around the Eddington rate. We therefore
suggest that advection-dominated flows may be more common than standard thin
disks in black hole systems. For certain ranges of radii and $\dot M$, no
stable steady state solution is possible. In these cases, we suggest that limit
cycle behavior may occur, leading to variability.
