The author develops a novel analysis method for QCD sum rules
(QCDSR) by applying the maximum entropy method (MEM) to arrive at
an analysis with less artificial assumptions than previously held.
This is a first-time accomplishment in the field. In this thesis, a
reformed MEM for QCDSR is formalized and is applied to the sum
rules of several channels: the light-quark meson in the vector
channel, the light-quark baryon channel with spin and isospin 1/2,
and several quarkonium channels at both zero and finite
temperatures. This novel technique of combining QCDSR with MEM is
applied to the study of quarkonium in hot matter, which is an
important probe of the quark-gluon plasma currently being created
in heavy-ion collision experiments at RHIC and LHC.
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