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.
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