RHESSI is the sixth in the NASA line of Small Explorer (SMEX) missions and the first managed in the Principal Investigator mode, where the PI is responsible for all aspects of the mission except the launch vehicle. RHESSI is designed to investigate particle acceleration and energy release in solar flares, through imaging and spectroscopy of hard X-ray/gamma-ray continua emitted by energetic electrons, and of gamma-ray lines produced by energetic ions. The single instrument consists of an imager, made up of nine bi-grid rotating modulation collimators (RMCs), in front of a spectrometer with nine cryogenically-cooled germanium detectors (GeDs), one behind each RMC. It provides the first high-resolution hard X-ray imaging spectroscopy, the first high-resolution gamma-ray line spectroscopy, and the first imaging above 100 keV including the first imaging of gamma-ray lines. The spatial resolution is as fine as ∼ 2.3 arc sec with a full-Sun (≳ 1°) field of view, and the spectral resolution is ∼ 1 10 keV FWHM over the energy range from soft X-rays (3 keV) to gamma-rays (17 MeV). An automated shutter system allows a wide dynamic range (>107) of flare intensities to be handled without instrument saturation. Data for every photon is stored in a solid-state memory and telemetered to the ground, thus allowing for versatile data analysis keyed to specific science objectives. The spin-stabilized (∼ 15 rpm) spacecraft is Sun-pointing to within ∼ 0.2° and operates autonomously. RHESSI was launched on 5 February 2002, into a nearly circular, 38° inclination, 600-km altitude orbit and began observations a week later. The mission is operated from Berkeley using a dedicated 11-m antenna for telemetry reception and command uplinks. All data and analysis software are made freely and immediately available to the scientific community.