Delphi (DEtector with Lepton, Photon and Hadron Identification) is one of the four experiments of the LEP (Large Electron Positron) collider at CERN. The detector is laid out to provide a nearly 4/spl pi/ coverage for charged particle tracking, electromagnetic, hadronic calorimetry and extended particle identification. The trigger system consists of four levels. The first two are synchronous with the BCO (beam cross over) and rely on hardwired control units, while the last two are performed asynchronously with respect to the BCO and are driven by the Delphi host computers. The aim of this paper is to give a comprehensive global view of the trigger system architecture, presenting in detail the first two levels, their various hardware components and the latest modifications introduced in order to improve their performance and make more user friendly the whole software user interface.< >