Magnetic resonance imaging (MRI) is a clinically important medical imaging modality due to its exceptional soft-tissue contrast. MRI was invented in the early 1970s. The first commercial scanners appeared about 10 years later. Noninvasive MRI studies are now supplanting many conventional invasive procedures. A 1990 study found that the principal applications for MRI are examinations of the head (40%), spine (33%), bone and joints (17%), and the body (10%). The percentage of bone and joint studies was growing in 1990. Although typical imaging studies range from 1 to 10 min, new fast imaging techniques acquire images in less than 50 msec. MRI research involves fundamental tradeoffs between resolution, imaging time, and signal-to-noise ratio (SNR). It also depends heavily on both gradient and receiver coil hardware innovations. In this section we provide a brief synopsis of basic nuclear magnetic resonance (NMR) physics. We then derive the k-space analysis of MRI, which interprets the received signal as a scan of the Fourier transform of the image. This powerful formalism is used to analyze the most important imaging sequences. Finally, we discuss the fundamental contrast mechanisms for MRI.