Computational algorithms relevant to the kinetic description of collisionless and collisional plasmas, as well as other physical systems with complex interactions, will be developed and applied. Specifically, algorithms that preserve geometric, conservative, and/or Hamiltonian structure upon discretization will be developed, analyzed, and extended. Newly developed codes will be further benchmarked against physical problems with known solutions. Applications to basic laboratory, fusion related, and space/astrophysical plasmas will be undertaken.