  Lattice QCD calculation of s-wave hadron scattering lengths in the channels
\pi-\pi, \pi-N, K-N, {\bar K}-N and N-N is carried out in the quenched QCD at
$\beta=6/g^2=5.7$. A variant of the method of wall sourceis developed for this
purpose, which reduces the computer time by a factor L^3 on an L^3xT lattice
compared to the conventional point source method and avoids the Fierz mixing
problem. A version of the method in which gauge configurations are not fixed to
any gauge can be extended to calculate disconnected quark loop con- tributions
in hadron two- and three-point functions. An analytical estimate of statistical
errors for this method is worked out, and the magnitude of errors without and
with gauge fixing is compared for the case of \pi-\pi four-point functions
calculated with the KS quark action. For \pi-\pi scattering both I=0 and 2
scattering lengths are evaluated using the KS and Wilson quark actions on a
12^3x20 lattice. For the same size of lattice, \pi-N, K-N and {\bar K}-N
scattering lenghts are calculated with the Wilson quark action. For the \pi-\pi
and \pi-N cases simulation results are consistent with the predictions of
current algebra and PCAC within one to two standard deviations up to quite
heavy quark masses corresponding to $m_\pi/m_\rho\approx 0.74$, while for the
K-N and {\bar K}-N cases the agreement is within a factor of two. For N-N scat-
tering simulations with the Wilson action on a 20^4 lattice with heavy quarks
with $m_\pi/m_\rho\approx 0.74-0.95$, where the deuteron is expected to become
unbound from a phenomenological study with one-boson exchange potentials, show
that the nucleon-nucleon force is attractive for both spin triplet and singlet
channels, and that the scattering lengths are substantially larger compared to
those for the \pi-\pi and \pi-N cases even for such heavy quarks.
