  Let $X$ be an irreducible smooth projective algebraic curve of genus $g \geq
2$ over the ground field $\bc$ and let $G$ be a semisimple simply connected
algebraic group. The aim of this paper is to introduce the notion of semistable
and stable parahoric torsors under a certain Bruhat-Tits group scheme $\mathcal
G$ and construct the moduli space of semistable parahoric $\mathcal
G$--torsors; we also identify the underlying topological space of this moduli
space with certain spaces of homomorphisms of Fuchsian groups into a maximal
compact subgroup of $G$. The results give a generalization of the earlier
results of Mehta and Seshadri on parabolic vector bundles. This is the final
version of the accepted paper.
