Researchers at the Technical University of Darmstadt were commissioned by the BSI to produce a study on the "Evaluation of lattice-based cryptographic methods" before the submission deadline for the NIST standardisation process. The aim of this study was to obtain an analysis of the lattice-based public key methods (key agreement, signature and encryption) that had been released up to that point. To do this, the first part initially compiled the theoretical foundations necessary to assess the security of lattice-based methods. The second part of the study consists of an overview of these methods and an evaluation of selected methods based on the results of the first part.