The scope of this work comprises the calculation and simulation of a Q-switched solid-state laser ignition source. This is part of the development project of an ignition laser which should replace the conventional spark plug in internal combustion engines. The demand for higher efficient and low emission engines for the production of electrical energy increased rapidly due to several environmental aspects. The most important benefit of the new alternative ignition system is the potential for ignition of very lean mixtures which results in lower emissions of nitrous oxides (NOx) and an increase in efficiency. The main topic of this work is the analysis and the simulation of such a Q-switched laser system. The calculations including all relevant parameters are based on the rate equations for a four-level laser system. The target audience of this book are mathematicians, physicists, other engineering students and researchers in the automotive industry.