This thesis introduces a novel discretization technique for solving hyperbolic conservation laws, called Mapped Tent Pitching (MTP) scheme. A tent pitching algorithm creates space-time domains, called tents, by vertically erecting canopies over spatial vertex patches. The structure of such a tent pitched space-time mesh is exploited by the MTP scheme to map these tents to a reference domain with a space-time tensor product structure. These domains are spatially discretized with a high order discontinuous Galerkin method, combined with a time stepping method. To obtain a robust method an entropy viscosity regularization is applied. This MTP scheme is implemented as part of this thesis based on the finite element library Netgen/NGSolve and tested with challenging problems like the Euler equations.