A full-field transmission X-ray microscope (TXM) operating continuously from 5 keV to 12 keV with fluorescence mapping capability has been designed and constructed at the Beijing Synchrotron Radiation Facility, a first-generation synchrotron radiation facility operating at 2.5 GeV. Spatial resolution better than 30 nm has been demonstrated using a Siemens star pattern in both absorption mode and Zernike phase-contrast mode. A scanning-probe mode fluorescence mapping capability integrated with the TXM has been shown to provide 50 p.p.m. sensitivity for trace elements with a spatial resolution (limited by probing beam spot size) of 20 µm. The optics design, testing of spatial resolution and fluorescence sensitivity are presented here, including performance measurement results.