The course will give a self-contained construction of Liouville CFT from Segal's axioms, using probability theory. The first part will be a review of Segal's definition of CFT, with a focus on the semigroup of annuli. Then, we will see how to quantise the semigroup with the Gaussian free field. Finally, we will construct Liouville CFT and reach a definition of conformal blocks. I will try to make some links with other approaches to CFT (e.g. VOAs), and keep some time for open questions related to the probabilistic construction.