This thesis focuses on the improvement of the Hermite-Fourier spectral method for solving kinetic plasma problems. In the first part of the thesis a novel dynamically adaptive techniques for changing the number of Hermite modes and Hermite basis are presented. Preconditioning of the problem and use of high-end scientific toolkit PETSc are discussed. The technique of changing the number of modes and preconditioning are believed to reduce computational time, while a change of basis improves robustness and numerical convergence of the method. The second part of the thesis focuses on paralellization strategies and performance analysis of the code implemented in the Fortran programming language.