These lecture notes illustrate the application of Dyson-Schwinger equations
in QCD. The extensive body of work at zero temperature and chemical potent
ial is represented by a selection of contemporary studies that focus on sol
ving the Bethe-Salpeter equation, deriving an exact mass formula in QCD tha
t describes light and heavy pseudoscalar mesons simultaneously, and the cal
culation of the electromagnetic pion form factor and the vector-meson elect
roproduction cross sections. These applications emphasize the qualitative i
mportance of the momentum-dependent dressing of elementary Schwinger functi
ons in QCD, which provides a unifying connection between disparate phenomen
a. They provide a solid foundation for an extension of the approach to nonz
ero temperature and chemical potential. The essential, formal elements of t
his application are described, and four contemporary studies are employed t
o exemplify the method and its efficacy. They study the demarcation of the
phase boundary for deconfinement and chiral symmetry restoration, the calcu
lation of bulk thermodynamic properties of the quark-gluon plasma, and the
response of pi- and rho- meson observables to T and mu. Along the way a con
tinuum order parameter for deconfinement is introduced, an anticorrelation
between the response of masses and decay constants to T and their response
to mis elucidated, and a (T, mu) mirroring of the slow approach of bulk the
rmodynamic quantities to their ultrarelativistic limit is highlighted. Thes
e effects too are tied to the momentum-dependent dressing of the elementary
Schwinger functions. (C) 1999 American Institute of Physics. [S1063-7796(9
9)00103-5].