  Direct links between generalized harmonic numbers, linear Euler sums and
Tornheim double series are established in a more perspicuous manner than is
found in existing literature. We show that every linear Euler sum can be
decomposed into a linear combination of Tornheim double series of the same
weight. New closed form evaluations of various Euler sums are presented.
Finally certain combinations of linear Euler sums that are reducible to Riemann
zeta values are discovered.
