STMX is a high-performance Common Lisp library for composable Transactional Memory (TM), a concurrency control mechanism aimed at making concurrent programming easier to write and understand. Instead of traditional lock-based programming, one programs with atomic memory transactions: if a memory transaction returns normally it is committed. If it signals an error, it is rolled back. Transactions can safely run in parallel in different threads, are re-executed from the beginning in case of conflicts or if consistent reads cannot be guaranteed, and effects of a transaction are not visible from other threads until committed. This gives freedom from deadlocks, automatic rollback on failure, and aims to resolve the tension between granularity and concurrency.