With masses comparable to that of the Sun and radii of about only ten kilometers, neutron stars are the most compact stars in the Universe. They offer a unique possibility of revealing the properties of superdense matter through a comparison of theoretical models to observations. This book describes all layers of neutron stars with the emphasis on their thermodynamics and composition. Theories of dense matter are reviewed and used to construct neutron star models. Separate chapters are devoted to hypothetical strange quark stars and exotic phases of dense matter in neutron star cores. The effects of strong magnetic fields in neutron star envelopes are discussed and the final chapter compares neutron star models to observations.