  We work out the algebraic Bethe ansatz for the worldsheet theory of the
$AdS_3\times S^3\times T^4$ superstring, and use it to derive the transfer
matrices for fundamental particles and bound states of the string and mirror
model. We also show how the Bethe equations and transfer matrices are modified
in the presence of an Abelian twist. These will be an important ingredient in
the exploration of the mirror thermodynamic Bethe ansatz equations recently
proposed by Frolov and Sfondrini, and their generalisation to twisted and
deformed models.
