The authors describe the important generalization of the original Weil
conjectures, as given by P. Deligne in his fundamental paper "La
conjecture de Weil II". The authors follow the important and beautiful
methods of Laumon and Brylinski which lead to a simplification of
Deligne's theory. Deligne's work is closely related to the sheaf
theoretic theory of perverse sheaves. In this framework Deligne's
results on global weights and his notion of purity of complexes obtain a
satisfactory and final form. Therefore the authors include the complete
theory of middle perverse sheaves. In this part, the l-adic Fourier
transform is introduced as a technique providing natural and simple
proofs. To round things off, there are three chapters with significant
applications of these theories.