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Explore the fundamentals of cosmography through gravitational wave standard sirens in this comprehensive lecture delivered as part of the Summer School on Gravitational-Wave Astronomy at the International Centre for Theoretical Sciences. Learn how gravitational wave observations can be utilized as powerful tools for measuring cosmic distances and understanding the expansion of the universe. Discover the theoretical foundations of standard sirens, their role in cosmological measurements, and how they complement traditional astronomical distance indicators. Examine the methodology for extracting cosmological parameters from gravitational wave detections and understand the unique advantages that these cosmic messengers offer for probing the universe's structure and evolution. Gain insights into current observational capabilities and future prospects for using gravitational wave astronomy to address fundamental questions in cosmology, including measurements of the Hubble constant and investigations into dark energy. This foundational lecture provides essential knowledge for understanding how gravitational wave detections are revolutionizing our approach to cosmological studies and opening new avenues for exploring the universe's properties through multi-messenger astronomy techniques.
