Explore the fascinating world of neutron stars and binary systems in this third lecture of the series on "The Astrophysics of Neutron Stars and Binaries" delivered by Dipankar Bhattacharya from Ashoka University, India. Delve into advanced concepts of astrophysics as part of the Summer School on Gravitational-Wave Astronomy organized by the International Centre for Theoretical Sciences. Learn about the potential sources of gravitational waves, focusing on continuous gravitational waves from rapidly spinning neutron stars and exotic sources like axion clouds around black holes. Gain insights into the latest developments in gravitational-wave astronomy and prepare for the upcoming observing runs of LIGO, Virgo, and KAGRA. This 1-hour 21-minute lecture is an essential component of a comprehensive program designed to expand knowledge in the field of gravitational-wave detection and analysis.