A very compact architecture has been developed for the first level Muon Trigger of the LHCb experiment that processes 40 millions of proton-proton collisions per second. For each collision, it receives 3.2 kBytes of data and it finds straight tracks within a 1.2 microseconds latency. The trigger implementation is massively parallel, pipelined and fully synchronous with the LHC clock. It relies on 248 high density Field Programable Gate arrays and on the massive use of multigigabit serial link transceivers embedded inside FPGAs.