The EEE (Extreme Energy Events) Project, conceived many years ago by its leader Antonino Zichichi, aims to study high-energy extensive air showers through the detection of the shower muon component by means of a network of tracking detectors, namely telescopes, installed in Italian High Schools. The Project is supported by the “Ministero dell’Istruzione, Universit` e Ricerca (MIUR)”, “Museo Storico della Fisica e Centro Studi e Ricerche E. Fermi”, “Istituto Nazionale di Fisica Nucleare (INFN)” and the European Organization for Nuclear Research (CERN). The single tracking telescope for a school is composed by 3 large (about 2 m^2 each) Multi-gap Resistive Plate Chambers (MRPC). Using a very high precision particle detector based on MRPCs allows a very high accuracy direction reconstruction for energetic showers, together with a very good temporal resolution. In its first phase the telescopes are going to be installed in 23 High Schools located in seven pilot towns all over Italy. In the near future, as soon as new fundings will be provided, the network will be upgraded adding new High Schools and towns. The first muon telescopes have been installed in two schools nearby Rome and in one school nearby Bologna, and are successfully running. By the end of the year 2007, other telescopes will be installed. Here we present the experimental apparatus and its tasks.