Mutual exclusion (mutex) is one of the most fundamental synchronization problems encountered in shared memory systems. It appears in all computer science first-degree curricula. This article presents nine mutex algorithms, each with its noteworthy features, spread over seven dates covering 1965-2020. Most of these algorithms are very well known and paved the way for new research directions. This article aims to present fundamental issues and basic principles that underlie the design of shared memory mutex algorithms in different contexts. So, differently from exhaustive surveys on shared memory mutex algorithms, it strives to give the reader a flavor of the many design facets of this still challenging problem.