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I will give an introductory overview of the theory recently proposed by David, Kupiainen, Rhodes and Vargas to give a rigourous probabilistic construction of Liouville CFT on the Riemann sphere. We will start from Polyakov's action and see how this can be assigned a meaning through the Gaussian multiplicative chaos of a Lebesgue-shifted Gaussian free field on the sphere. Time permitting, I will show one calculation hinting at the integrability of the model.