[en] When studying 2d quantum gravity several approaches can be used in complementary ways. For example the matrix models (discretization) is powerful and gives a non-perturbative definition, while Liouville theory (continuous approach) offer a more transparent physical interpretation (states are easier to identify, for example from BRST cohomology). These notes grew up from lectures by Atish Dabholkar, and from discussions with him and his students. This review is still a work in progress. Content: 1 - Introduction; 2 - Conformal field theory (Coordinates, Quasi-primary fields, Operator product expansion, Free scalar field, Vertex operators, Rational and non-rational CFT, Minimal models); 3 - Correlation functions (Conformal blocks); 4 - Liouville theory, Two-dimensional gravity (Pure gravity, Action and symmetries, Equations of motion, Partition functions, Equations of motion and stress-energy tensor, Conformal matter, Conformal gauge, Gauge fixing, Ghost action, Emerging Weyl symmetry, Measures, General properties, Scalar and vector field measures, Gravitational metric measure, Computing path integrals); 5 - Liouville effective action for quantum gravity with conformal matter (Conformal anomaly, General expression, Adding the cosmological constant term, Derivation of the classical Liouville action, Integrating the conformal anomaly, Partition function and transformation properties, Application to 2d gravity, Few properties of the classical Liouville action, Central charge, Polyakov action and critical string theory, Changing the Liouville mode measure, Ansatz for the jacobian, Explicit computation, Summary, Interactions with matter, Non-local effective action, Comment on Liouville action status, Gravitational anomaly); 6 - Properties of Liouville action (Definitions, Coordinates, Values of the central charge, Partition function at fixed area, Critical exponents, Equations of motion and classical solutions, Equations, Classical solutions, Backluend transformation, Complex coordinates, General computations, From the cylinder to the plane, Lorentzian theory, Hamiltonian formalism, Mini-superspace, States, Semi-classical limit, Semi-classical action, Correlation functions on the sphere, Ultra-local approximation); 7 - Quantization (Canonical quantization, Operator formalism, Mini-superspace quantization, Canonical quantization, Wave functions, States, Correlation functions); 8 - Liouville duality (Dual cosmological constant, Quantum theory); 9 - Correlation functions (2-point function, 3-point function and DOZZ formula, 2-point function limit, Reflection coefficient); 10 - Extensions, Conformal bootstrap (Hypothesis and setup, Teschner's recursion relations, Derivation, First solution, Second solution, Crossing symmetry, Modular invariance); 11 - Runkel-Watts-Schomerus theories (Three-point function from analytical continuation, Limit from minimal models, Continuous orbifold); 12 - Complex Liouville theory (Lagrangian study, Liouville theory, Correlation functions, The fake-identity operator); 13 - Time-like Liouville theory (Definition, Equations of motion and semi-classical limit, Classical solutions, States, Mini-superspace, Canonical quantization, Naive wave functions, Self-adjoint extension, States, Correlation functions); 14 - Effective actions for 2d quantum gravity (General properties, Kaehler potential, Effective actions, The area action, Liouville action, Mabuchi action, Aubin-Yau action); 15 - Mabuchi action (Critical exponents); 16 - Boundary Liouville theory (Action, Correlation functions); 17 Applications, Cosmology; 18 - Appendices (Conventions, General relativity, Matter models, Mathematical tools, Special functions, References).