In this thesis the theory needed to calculate linear and nonlinear optical properties of crystals are presented with applications to atomically thin materials in mind. This covers (among other things) ab initio tight-binding parametrisation, crystal symmetry considerations, a rigorous introduction of linear and nonlinear single-particle response functions, the Bethe-Salpeter equation, the Rytova-Keldysh potential and expressions for linear and nonlinear excitonic response functions. This enables the description of nonlinear phenomena such as second-harmonic generation and optical rectification. This theory is applied on mainly monolayer In$_2$Se$_2$ and MoS$_2$. First-order responses are successfully calculated in both the single-particle and excitonic cases. In one of the two approaches to the second-order response, a computational problem is identified. A solution for this is proposed for the the single-particle case, but invalidates one half of the calculated excitonic second-order response.\par Comparisons of theory with four experiments found in literature is presented and limited agreement is found using the non-faulty half of the excitonic calculations. An automatisation procedure to enable large scale calculations on other materials is proposed and implemented with limited success. Automatic symmetry detection and nonzero tensor element calculation is successfully implemented.