This chapter focuses on some ‘engineering relevant’ partial differential equations (PDEs). As most PDEs cannot be solved analytically, we give a brief overview of computational methods. Therefore, we present for one specific mechanical problem, the boundary value problem of linear elastostatics, the strong form and weak form, which are the basis for different computational methods. In this context we also discuss the energy approach to the solution of a BVP as many engineering problems can be described through the definition of an energy. As will be seen later, energy approaches are also well suited for the machine learning based solutions of PDEs. Section 3.2 concerns about second-order PDEs. As representative elliptic PDEs, we consider the Laplace, Poisson, Helmholtz and linear elasticity equations. Subsequently, we present the convection-diffusion and diffusion equation as well as the Navier-Stokes equations, which are parabolic PDEs. The hyperbolic PDEs solved within a machine learning approach in this book include the wave equation, Burger’s equation and linear elastodynamics. As examples for higher-order PDEs, we consider two classical fourth-order PDEs in structural analysis: The Euler-Bernoulli beam and the Kirchhoff plate. The last section of this chapter focuses on energy methods. Firstly, we give a brief overview of hyperelasticity before presenting two popular coupled problems: Flexoelectricity and phase field models; the latter one is mainly applied to model material failure.