  As the endpoints of massive star evolution, neutron stars are enigmatic
celestial objects characterized by extremely dense and exotic nuclear matter,
magnetospheres with positrons (antimatter), rapid rotation and ultra-strong
magnetic fields. Such an extreme environment has provided an accessible
astrophysical laboratory to study physics under conditions unattainable on
Earth and to tackle a range of fundamental questions related to: the aftermath
of stellar evolution and the powerful explosions of massive stars, the equation
of state and physics of some of the most exotic and magnetic stars in the
Universe, the workings of the most powerful particle accelerators in our Galaxy
and beyond, and the sources of gravitational waves that are yet to be detected.
Recent observations revealed a great diversity of neutron stars, including
ultra-strongly magnetized pulsars, referred to as "magnetars", and unusual
types of accreting X-ray pulsars. In this white paper, we highlight the
prospects of the upcoming X-ray mission, ASTRO-H, in studying these highly
magnetized neutron stars.
