  We present global solutions that describe advection-dominated accretion flows
around black holes. The solutions are obtained by numerically solving a set of
coupled ordinary differential equations corresponding to a steady axisymmetric
height-integrated flow. The solutions satisfy consistent boundary conditions at
both ends. We obtain well-behaved transonic solutions for a wide range of
values of the viscosity parameter $\alpha$, from 0.001 to 0.3. We do not find
any need for shocks in our solutions, and disagree with previous claims that
viscous accretion flows with low values of $\alpha$ must have shocks. We see a
qualitative difference between solutions with low values of the viscosity
parameter, $\alpha\ \sles\ 0.01$, and those with large values, $\alpha\sgreat\
0.01$. The solutions with low $\alpha$ have their sonic transitions occurring
close to the radius of the marginally bound orbit. These flows are
characterized by regions of super-Keplerian rotation, and have pressure maxima
outside the sonic point. The solutions are similar in many respects to the
hydrostatic thick tori developed previously as models of active galactic
nuclei. In contrast, the solutions with large $\alpha$ have sonic transitions
farther out, close to or beyond the marginally stable orbit, and have no
super-Keplerian rotation or pressure maxima. We believe these flows will be
nearly quasi-spherical down to the sonic radius and will not have empty funnels
along the rotation axis. The large $\alpha$ solutions are more likely to be
representative of real systems.
