For the interested reader, this article contains pointers to literature on the Alpha miner.
For the interested reader pointers follow to the scientific papers that describe in great detail how the Alpha miner works. Note that this is extra material and this is not required for the course.
In short, the differences between the four algorithms are that the Alpha miner is of course the first and most basic implementation. The Alpha+ algorithm is an extension on the Alpha miner which can deal with short-loops and self-loops. The Alpha++ algorithm is again an extension, which is able to find additional non-free choice constructs (e.g. can discover more complex patterns). The Alpha# algorithm can also discover several invisible tasks that are not observable but which do influence the control flow.