Chapter 1, on the "Compilation of Polychronous Data-Flow Equations", gives a thorough presentation of the program analysis and code generation techniques present in Polychrony, a compiler for the data-flow synchronous language Signal. Introduced in the late 1980s, Signal and its polychronous model of computation stand among the most developed concepts of synchronous programming. It allows to model concurrent embedded software architectures using high-level multi-clocked synchronous data-flow equations. The chapter defines the formal methodology consisting of all required program analysis and transformation techniques to automatically generate the sequential or concurrent code suiting the targer architecture (embedded or distributed) or compilation goals (modularity or performance).