  Multiparametric quantum deformations of $gl(2)$ are studied through a
complete classification of $gl(2)$ Lie bialgebra structures. From them, the
non-relativistic limit leading to harmonic oscillator Lie bialgebras is
implemented by means of a contraction procedure. New quantum deformations of
$gl(2)$ together with their associated quantum $R$-matrices are obtained and
other known quantizations are recovered and classified. Several connections
with integrable models are outlined.
