Latin squares have been studied since the days of Euler. After some overview on the history and background, an effort for a complete enumeration of special types of Latin squares of order 13, by as completely automated means as possible (which is currently actually not possible), will be presented and evaluated. The main method here is Cube-and-Conquer, a kind of 2-stage SAT-solving (as invented by the presenter). Quite some fine-tuning of representation and choice of solver was needed, and will be discussed (at some high level).