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Variational integrators are a special kind of geometric discretisationmethods applicable to any system of differential equations that obeys aLagrangian formulation. In this thesis, variational integrators are developedfor several important models of plasma physics: guiding centre dynamics(particle dynamics), the Vlasov-Poisson system (kinetic theory), and idealmagnetohydrodynamics (plasma fluid theory). Special attention is given tophysical conservation laws like conservation of energy and momentum.  Most systems in plasma physics do not possess a Lagrangian formulation towhich the variational integrator methodology is directly applicable. Thereforethe theory is extended towards nonvariational differential equations by linkingit to Ibragimov's theory of integrating factors and adjoint equations. Itallows us to find a Lagrangian for all ordinary and partial differentialequations and systems thereof. Consequently, the applicability of variationalintegrators is extended to a much larger family of systems than envisaged inthe original theory. This approach allows for the application of Noether'stheorem to analyse the conservation properties of the system, both at thecontinuous and the discrete level.  In numerical examples, the conservation properties of the derived schemes areanalysed. In case of guiding centre dynamics, momentum in the toroidaldirection of a tokamak is preserved exactly. The particle energy exhibits anerror, but the absolute value of this error stays constant during the entiresimulation. Therefore numerical dissipation is absent. In case of the kinetictheory, the total number of particles, total linear momentum and total energyare preserved exactly, i.e., up to machine accuracy. In case ofmagnetohydrodynamics, the total energy, cross helicity and the divergence ofthe magnetic field are preserved up to machine precision.

Variational Integrators in Plasma Physics