  Single crystals of BaFe$_2$As$_2$ and (Ba$_{0.55}$K$_{0.45}$)Fe$_2$As$_2$
have been grown out of excess Sn with 1% or less incorporation of solvent. The
crystals are exceptionally micaceous, are easily exfoliated and can have
dimensions as large as 3 x 3 x 0.2 mm$^3$. The BaFe$_2$As$_2$ single crystals
manifest a structural phase transition from a high temperature tetragonal phase
to a low temperature orthorhombic phase near 85 K and do not show any sign of
superconductivity down to 1.8 K. This transition can be detected in the
electrical resistivity, Hall resistivity, specific heat and the anisotropic
magnetic susceptibility. In the (Ba$_{0.55}$K$_{0.45}$)Fe$_2$As$_2$ single
crystals this transition is suppressed and instead superconductivity occurs
with a transition temperature near 30 K. Whereas the superconducting transition
is easily detected in resistivity and magnetization measurements, the change in
specific heat near $T_c$ is small, but resolvable, giving $\Delta C_p/\gamma
T_c \approx 1$. The application of a 140 kOe magnetic field suppresses $T_c$ by
only $\sim 4$ K when applied along the c-axis and by $\sim 2$ K when applied
perpendicular to the c-axis. The ratio of the anisotropic upper critical
fields, $\gamma = H_{c2}^{\perp c} / H_{c2}^{\| c}$, varies between 2.5 and 3.5
for temperatures down to $\sim 2$ K below $T_c$.
