  Wormholes are outstanding solutions of Einstein's General Relativity. They
were worked out in the late 1980's by Morris and Thorne, who have figured out a
recipe that wormholes must obey in order to be traversable, that is, safely
crossed by travelers. A remarkable feature is that General Relativity Theory
wormholes must be filled by {\it exotic matter}, which Morris and Thorne define
as matter satisfying $-p_r>\rho$, in which $p_r$ is the radial pressure and
$\rho$ is the energy density of the wormhole. In the present article, we
introduce, for the first time in the literature, traversable wormhole solutions
of Einstein's Unimodular Gravity Theory. Unimodular Gravity was proposed by
Einstein himself as the theory for which the field equations are the traceless
portion of General Relativity field equations. Later, Weinberg has shown that
this approach elegantly yields the solution of the infamous cosmological
constant problem. The wormhole solutions here presented satisfy the metric
conditions of "traversability" and remarkably evade the exotic matter
condition, so we can affirm that Unimodular Gravity wormholes can be filled by
ordinary matter.
