Neutron star,with masses about the sun and radii of about 10Km, have internal matter-densities which reaches atomic nuclear densities. Because of their strong magnetization and rapid rotation they have become one of the central pillars of theoretical and observational astrophysics. Pulsar observations are currently providing a glimpse of various new states of matter under extreme conditions possibly present in compact stars like neutron stars. This book reinforces the physical understanding of matter density variation inside the neutron star,neutron capture nucleosynthesis in massive stars towards the formation of neutron star as well as the surface magnetic field strength towards the nature of different types of neutron stars such as isolated, radio-pulsars, magnetars, etc. This book concludes with a chapter on "recent developments" with an objective to provide the current understanding of the physics of neutron stars and pulsars and thereby providing insight into the important unsolved problems. This book is suitable for graduate students, and for researchers in physics and astrophysics.