  We have completely determined the Fermi surface in KFe$_2$As$_2$ via de
Haas-van Alphen (dHvA) measurements. Fundamental frequencies $\epsilon$,
$\alpha$, $\zeta$, and $\beta$ are observed in KFe$_2$As$_2$. The first one is
attributed to a hole cylinder near the X point of the Brillouin zone, while the
others to hole cylinders at the $\Gamma$ point. We also observe magnetic
breakdown frequencies between $\alpha$ and $\zeta$ and suggest a plausible
explanation for them. The experimental frequencies show deviations from
frequencies predicted by band structure calculations. Large effective masses up
to 19 $m_e$ for $B \parallel c$ have been found, $m_e$ being the free electron
mass. The carrier number and Sommerfeld coefficient of the specific heat are
estimated to be 1.01 -- 1.03 holes per formula unit and 82 -- 94
mJmol$^{-1}$K$^{-2}$, respectively, which are consistent with the chemical
stoichiometry and a direct measure of 93 mJmol$^{-1}$K$^{-2}$ [H. Fukazawa
\textit{et al}., J. Phys. Soc. Jpn. \textbf{80SA}, SA118 (2011)]. The
Sommerfeld coefficient is about 9 times enhanced over a band value, suggesting
the importance of low-energy spin and/or orbital fluctuations, and places
KFe$_2$As$_2$ among strongly correlated metals. We have also performed dHvA
measurements on Ba$_{0.07}$K$_{0.93}$Fe$_2$As$_2$ and have observed the
$\alpha$ and $\beta$ frequencies.
