  We present a high throughput computational search for altermagnetism in
two-dimensional (2D) materials based on the Computational 2D Materials Database
(C2DB). We start by showing that the symmetry requirements for altermagnetism
in 2D are somewhat more strict compared to bulk materials and applying these
yields a total of 7 altermagnets in the C2DB. The collinear ground state in
these monolayers are verified by spin spiral calculations using the generalized
Bloch theorem. We focus on four $d$-wave altermagnetic materials belonging to
the $P2_1'/c'$ magnetic space group - RuF$_4$, VF$_4$, AgF$_2$ and OsF$_4$. The
first three of these are known experimentally as van der Waals bonded bulk
materials and are likely to be exfoliable from their bulk parent compounds. We
perform a detailed analysis of the electronic structure and non-relativistic
spin splitting in $k$-space exemplified by RuF$_4$. The magnon spectrum of
RuF$_4$ is calculated from the magnetic force theorem and it is shown that the
symmetries that enforce degenerate magnon bands in anti-ferromagnets are absent
in altermagnets and give rise to the obtained non-degenerate magnon spectrum.
We then include spin-orbit effects and show that these will dominate the
splitting ofmagnons in RuF$_4$. Finally, we provide an example of $i$-wave
altermagnetism in the 2H phase of FeBr$_3$.
