  We present single- and multiple-quantum correlation $J$-spectroscopy detected
in zero ($<\!\!1$~$\mu$G) magnetic field using a \Rb vapor-cell magnetometer.
At zero field the spectrum of ethanol appears as a mixture of \carbon
isotopomers, and correlation spectroscopy is useful in separating the two
composite spectra. We also identify and observe the zero-field equivalent of a
double-quantum transition in ${}^{13}$C$_2$-acetic acid, and show that such
transitions are of use in spectral assignment. Two-dimensional spectroscopy
further improves the high resolution attained in zero-field NMR since selection
rules on the coherence-transfer pathways allow for the separation of otherwise
overlapping resonances into distinct cross-peaks.
