“Topological order” is a concept proposed in the 90’s by X.-G. Wen to describe the special kind of order at play in the fractional quantum Hall effect. The simplest model of topological order is the famous toric code. It is a very simple example of bosonic topological order, i.e. a model in which the microscopic degree of freedom are local and bosonic. During a recent PhD thesis, we have computed the exact partition function of all these models featuring bosonic topological order (based on Hamiltonians that are sums of local commuting projectors) and found that it is almost that of two decoupled one-dimensional (1D) Potts models. We now wish to extend this work to another type of topological order, namely 2D fermionic topological order. The main difference is that instead of starting from a lattice model in which the microscopic degrees of freedom are bosonic and local, one starts with fermionic microscopic dofs. In this internship, we will explore the physics of 2D fermionic topological order. We will get familiar with the 2D fermionic toric code, compute the degeneracy of its energy levels and from there obtain the partition function and study other finite-temperature properties such as entanglement entropy (or mutual information) and Wegner-Wilson loops. This will require getting familiar with mathematical concepts such as projective super fusion categories.