  We study the physics of dilute magnetic impurities in a two-dimensional
altermagnetic metal. We first discuss the Kondo problem. Although the spin
degeneracy is broken in an altermagnetic metal, we show that the
antiferromagnetic Kondo coupling still flows to the strong coupling regime at
low energies in terms of the one-loop renormalization-group equation. To study
the ground-state properties, we employ the variational wavefunction approach.
We find that the impurity spin is completely screened at long distances, in
contrast to the usual antiferromagnet. The $d$-wave nature of the Fermi surface
in an altermagnetic metal is reflected in the correlation between the impurity
and conduction electron spins, which exhibits the $C_{4z}$ symmetry of the
altermagnet at long distances. The spin correlation decays as $1/r^3$ at long
distances, and its amplitude oscillates with four different periods due to the
anisotropic Fermi surfaces. Moreover, the values of these periods depend on the
direction of observation. Next, we calculate the RKKY interaction which is of
an anisotropic Heisenberg type. This anisotropic RKKY interaction also exhibits
the $C_4$ symmetry at long distances due to the $d$-wave nature of the Fermi
surface. In addition, the transverse and longitudinal components of the RKKY
interactions posses distinct periods of oscillations.
