Abstract : Aims: We present observations of the Orion Bar photodissociation region (PDR) obtained with the SPIRE instrument on-board Herschel. Methods: We obtained SPIRE Fourier-transform spectrometer (FTS) sparse sampled maps of the Orion bar. Results: The FTS wavelength coverage and sensitivity allow us to detect a wealth of rotational lines of CO (and its isotopologues), fine structure lines of C and N+, and emission lines from radicals and molecules such as CH+, CH, H2O or H2S. For species detected from the ground, our estimates of the column densities agree with previously published values. The comparison between 12CO and 13CO maps shows particularly the effects of optical depth and excitation in the molecular cloud. The distribution of the 12CO and 13CO lines with upper energy levels indicates the presence of warm (~100-150 K) CO. This warm CO component is a significant fraction of the total molecular gas, confirming previous ground based studies. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.