The kinetics of intrinsic and dopant-enhanced solid-phase epitaxy (SPE) is studied in amorphous germanium $(a\text{-Ge})$ layers formed by ion implantation on $⟨100⟩$ Ge substrates. The SPE rates were measured with a time-resolved reflectivity (TRR) system between 300 and $540\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$ and found to have an activation energy of $(2.15\ifmmode\pm\else\textpm\fi{}0.04)\text{ }\text{eV}$. To interpret the TRR measurements the refractive indices of the $a\text{-Ge}$ layers were measured at the two wavelengths used, 1.152 and $1.532\text{ }\ensuremath{\mu}\text{m}$. For the first time, SPE rate measurements on thick $a\text{-Ge}$ layers $(>3\text{ }\ensuremath{\mu}\text{m})$ have also been performed to distinguish between bulk and near-surface SPE growth rate behavior. Possible effects of explosive crystallization on thick $a\text{-Ge}$ layers are considered. When H is present in $a\text{-Ge}$ it is found to have a considerably greater retarding effect on the SPE rate than for similar concentrations in $a\text{-Si}$ layers. Hydrogen is found to reduce the preexponential SPE velocity factor but not the activation energy of SPE. However, the extent of H indiffusion into $a\text{-Ge}$ surface layers during SPE is about one order of magnitude less than that observed for $a\text{-Si}$ layers. This is thought to be due to the lack of a stable surface oxide on $a\text{-Ge}$. Dopant-enhanced kinetics was measured in $a\text{-Ge}$ layers containing uniform concentration profiles of implanted As or Al spanning the concentration regime $1--10\ifmmode\times\else\texttimes\fi{}{10}^{19}/{\text{cm}}^{\ensuremath{-}3}$. Dopant compensation effects are also observed in $a\text{-Ge}$ layers containing equal concentrations of As and Al, where the SPE rate is similar to the intrinsic rate. Various SPE models are considered in light of these data.