  We study two-dimensional $d$-wave altermagnetic metals taking into account
the presence of substrate-induced Rashba spin-orbit coupling. We consider the
altermagnet bandstructure using a 2D band Hamiltonian near the $\Gamma$ point
under external magnetic field. It is shown that time-reversal-symmetry breaking
due to altermagnetism, together with Rashba coupling and external magnetic
field, can result in non-trivial band topology. The topological phases can be
tuned by magnetic field strength and directions, and are classified by their
Chern numbers. Furthermore, we investigate the charge response by computing the
full optical conductivity tensor with and without magnetic field. In
particular, we focus on magneto-optical responses, which are the
finite-frequency analog of the Berry curvature-induced anomalous Hall
conductivity. Finally, using experimentally realistic parameters for RuO$_2$,
we estimate the Faraday angle in the absence of magnetic fields.
