  We explore the possibilities for spin-singlet superconductivity in newly
discovered altermagnets. Investigating $d$-wave altermagnets, we show that
finite-momentum superconductivity can easily emerge in altermagnets even though
they have no net magnetization, when the superconducting order parameter also
has $d$-wave symmetry with nodes coinciding with the altermagnet nodes.
Additionally, we find a rich phase diagram when both altermagnetism and an
external magnetic field are considered, including superconductivity appearing
at high magnetic fields from a parent zero-field normal state.
