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This lecture covers the purpose and applications of X-ray Photon Correlation Spectroscopy (XPCS) in materials science, soft-matter science, and condensed-matter physics. XPCS provides insights into temporal fluctuations and correlations of structures within materials, making it suitable for studying complex systems like soft matter, colloids, glasses, and phase transitions. The lecture explains how XPCS analyzes the progress of coherent x-ray scattering patterns to gain insights into nanoscale structures' movement, interactions, and fluctuations. It also discusses the spatial arrangement of scattering features within samples and how they evolve over time. The lecture concludes by highlighting the limitations of XPCS until recently and the advancements in temporal resolution achieved at DLSRs, enabling the study of systems with characteristic time-scales like magnetic spin reorientation, ferroelectric-domain switching, and structural phase transitions.