We present a stepwise formal development of the Petersonrsquos mutual exclusion algorithm using Event B. We use a bottom-up approach where we introduce the parallel composition of subsystems which are separately specified. First, we specify subsystems as B abstract systems; then we compose the subsystems to get a first abstract solution for the mutual exclusion. This solution is improved to obtain the Petersonrsquos algorithm. This is achieved by refinement and composition of the former abstract subsystems. Therefore the result is formally proved on the basis of correctness (safety) properties added to the invariant. Atelier B (a B prover) is used to check completely the development.