This thesis presents an investigation into inertial confinement fusion through mathematical models and computer simulations. Salient features affecting fusion are identified, in both energy absorption and fusion gains. Mathematical tools are applied to a directed investigation into plasma structure. Parameters such as these involved in electromagnetic energy absorption are identified first, and the next step is to model the immediate response of the plasma to this energy input, with a view to how this may be advantageous to initiating fusion. Models are developed that best suit plasma behaviour. The parameters are presented graphically against time and distance into a small plasma fuel pellet. It is noted how field density and ions form undulations through the plasma. Types of plasma fuels are discussed with regards to their key parameters. Computations are performed using the laser driven inertial energy option based on volume ignition with the natural adiabatic self-similarity compression and expansion hydrodynamics. The relative merits of each fuel are discussed against the parameters of density, volume and energy input versus fusion gains. / Master of Science (Hons)