High-pressure science has experienced tremendous growth, particularly since the 1990s. With developments in static and dynamic compression techniques, extreme pressure and temperature conditions can now be produced and carefully controlled over a wide range. Moreover, a new generation of analytical probes, many based on third-generation synchrotron radiation sources, have been developed and can now be applied for accurate determination of the structural, dynamical, and electronic properties ofmatter under extreme conditions. This course on high pressure science was held at the International School of Physics "Enrico Fermi" School in July 2001. It spans fundamental physics and chemistry, materials science and technology, the geosciences, planetary science and astrophysics, as well as biology.