Finsler geometries give natural generalisations of Riemannian geometries, hence possible natural extensions of their applications. Many of those make use of symmetries, depending on the physical system they want to model. In this book we propose a simple method of imposition of symmetries in Finsler metrics and make use of it to derive the general form of the spherically and axially symmetric Finsler metrics in three and four dimensions. Finally, to give an example of such an application, we derive a spherically symmetric perturbative non-Riemannian solution for a possible Finsler extension of General Relativity.