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In this comprehensive volume, the authors introduce some of the most important recent developments at the intersection of probability theory and mathematical physics, including the Gaussian free field, Gaussian multiplicative chaos and Liouville quantum gravity. This is the first book to present these topics using a unified approach and language, drawing on a large array of multi-disciplinary techniques. These range from the combinatorial (discrete Gaussian free field, random planar maps) to the geometric (culminating in the path integral formulation of Liouville conformal field theory on the Riemann sphere) via the complex analytic (based on the couplings between Schramm-Loewner evolution and the Gaussian free field). The arguments (currently scattered over a vast literature) have been streamlined and the exposition very carefully thought out to present the theory as much as possible in a reader-friendly, pedagogical yet rigorous way, suitable for graduate students as well as researchers.