  This is my PhD thesis supervised by Professor Jerzy Weyman. A symmetric
quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$
equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The
involution allows us to define a nondegenerate bilinear form $<,>$ on a
representation $V$ of $Q$. We shall say that $V$ is orthogonal if $<,>$ is
symmetric and symplectic if $<,>$ is skew-symmetric. Moreover we define an
action of products of classical groups on the space of orthogonal
representations and on the space of symplectic representations. So we prove
that if $(Q,\sigma)$ is a symmetric quiver of finite type or of tame type then
the rings of semi-invariants for this action are spanned by the semi-invariants
of determinantal type $c^V$ and, in the case when matrix defining $c^V$ is
skew-symmetric, by the Pfaffians $pf^V$.
