1. Introduction and physics background

2. Stochastic quantization and SPDE

3. Mean field limits for coupled stochastic dynamics

4. Da Prato–Debussche and Mourrat–Weber arguments for dynamical $\Phi_{2}^{4}$

5. Mean field limit of dynamical linear $\sigma$-model in 2D

7. Exact correlation formulae for some $O(N)$ invariant observables

8. Convergence of (renormalized) linear $\sigma$-model to Gaussian free field in 3D

9. Discussions on possible future directions