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With its unique combination of enormous light gathering power and unprecedented spatial resolution (thanks to state-of-the-art adaptive optics), the ELT is set to revolutionise observational astrophysics. HARMONI – the ELT's integral field spectrograph - will provide spatially resolved spectroscopy of a wide variety of astronomical sources, ranging from solar system objects to the most distant galaxies ever observed. Extremely sensitive medium resolution spectroscopy will open new ways of understanding the physical processes throughout the history of the Universe. By using line strengths and ratios, together with Doppler shifts, HARMONI observations can deduce the morphology, as well as the kinematics, chemical composition, and physical characteristics (density, temperature, etc.) at high angular resolution. The talk will provide an introduction to the ELT, and showcase some of the salient observations where HARMONI@ELT can have a huge impact.