Mutual exclusion is perhaps the most prevalent form of coordination in multiprocessor programming. This chapter covers classical mutual exclusion algorithms that work by reading and writing shared memory. Although these algorithms are not used in practice, we study them because they provide an ideal introduction to the kinds of algorithmic and correctness issues that arise in every area of synchronization. The chapter also provides an impossibility proof. This proof teaches us the limitations of solutions to mutual exclusion that work by reading and writing shared memory, and will help to motivate the real-world mutual exclusion algorithms that appear in later chapters. This chapter is one of the few that contains proofs of algorithms. Though the reader should feel free to skip these proofs, it is very helpful to understand the kind of reasoning they present, because we can use the same approach to reason about the practical algorithms considered in later chapters.