  This book chapter explores key aspects of neutron stars, pulsar glitches,
tidal deformability, fast pulsars, the equation of state, and strange quark
matter stars. Challenges in directly measuring neutron star radius have led to
reliance on spectroscopic and timing techniques, with uncertainties addressed
through careful source selection and theoretical modeling. Pulsar glitches
reveal insights into the equation of state through angular momentum transfer
within the neutron star. Tidal deformability is crucial in gravitational-wave
astronomy, exemplified by the GW170817 event. Fast pulsars, instrumental in
astrophysical testing, are classified into ordinary pulsars, millisecond
pulsars, and magnetars. The EOS is vital for understanding neutron star
internal structure, explored through various models. The chapter delves into
the theoretical framework for rotating neutron stars, addressing uniform and
differential rotation scenarios and their impacts on mass and radius.
Additionally, the intriguing concept of quark stars and strange dwarfs is
investigated. The various topics discussed in this book chapter contribute to a
broader understanding of dense matter physics, astrophysical phenomena, and the
potential for transformative discoveries through advanced observational
techniques and technologies like gravitational wave detectors, radio
telescopes, and X-ray telescopes.
