This workshop is part of the thematic six-weeks program "Quantum gravity, random geometry and holography" held at Institut Henri Poincaré, Paris (program main page) The workshop will be devoted to quantum gravity approaches in two, three, and four dimensions, with an emphasis on the random geometry point of view. In the tradition of the conference series ``Quantum Gravity in Paris'', we aim at bringing together researchers working on various approaches to quantum gravity, fostering an open minded exchange of ideas and techniques, to be continued in the weeks after the workshop.