  In this paper we define odd dimensional unitary groups $U_{2n+1}(R,\Delta)$.
These groups contain as special cases the odd dimensional general linear groups
$GL_{2n+1}(R)$ where $R$ is any ring, the odd dimensional orthogonal and
symplectic groups $O_{2n+1}(R)$ and $Sp_{2n+1}(R)$ where $R$ is any commutative
ring and further the first author's even dimensional unitary groups
$U_{2n}(R,\Lambda)$ where $(R,\Lambda)$ is any form ring. We classify the
E-normal subgroups of the groups $U_{2n+1}(R,\Delta)$ (i.e. the subgroups which
are normalized by the elementary subgroup $EU_{2n+1}(R,\Delta)$), under the
condition that $R$ is either a semilocal or quasifinite ring with involution
and $n\geq 3$. Further we investigate the action of $U_{2n+1}(R,\Delta)$ by
conjugation on the set of all E-normal subgroups.
