Lectures given at a Summer School in Mexico: 2002 Extensive Air Showers and Ultra High Energy Cosmic Rays

Abstract. This paper is intended to be pedagogic. The first part is devoted to a brief exposition of the physics associated with the development of extensive air showers. This is seen as being relevant to any student beginning studies in this field. The latter part of the paper deals with methods of detection of extensive air showers, in a general way, and with results on the energy spectrum, arrival direction and mass distribution of cosmic rays of energy above 1018 eV. Finally, proposals for explaining the anomalous existence of the very highest energy cosmic rays are briefly discussed and forthcoming methods of detection through the Pierre Auger Observatory and the Extreme Universe Space Observatory (EUSO) are described shortly