The book gives an extended review of theoretical and observational aspects of neutron star physics. With masses comparable to that of the Sun and radii of about ten kilometres, neutron stars are the densest stars in the Universe. This book describes all layers of neutron stars, from the surface to the core, with the emphasis on their structure and equation of state. Theories of dense matter are reviewed, and used to construct neutron star models. Hypothetical strange quark stars and possible exotic phases in neutron star cores are also discussed. Also covered are the effects of strong magnetic fields in neutron star envelopes.