  We consider a compact hyperbolic tetrahedron of a general type. It is a
convex hull of four points called vertices in the hyperbolic space
$\mathbb{H}^3$. It can be determined by the set of six edge lengths up to
isometry. For further considerations, we use the notion of edge matrix of the
tetrahedron formed by hyperbolic cosines of its edge lengths.
  We establish necessary and sufficient conditions for the existence of a
tetrahedron in $\mathbb{H}^3$. Then we find relations between their dihedral
angles and edge lengths in the form of a cosine rule. Finally, we obtain exact
integral formula expressing the volume of a hyperbolic tetrahedron in terms of
the edge lengths. The latter volume formula can be regarded as a new version of
classical Sforza's formula for the volume of a tetrahedron but in terms of the
edge matrix instead of the Gram matrix.
