Title page -- Preface -- Contents -- Finite Field Experiments -- K3 Surfaces of Picard Rank One Which Are Double Covers of the Projective Plane -- Beilinson Conjectures in the Non-Commutative Setting -- Looking for Rational Curves on Cubic Hypersurfaces -- Abelian Varieties over Finite Fields -- How to Obtain Global Information from Computations over Finite Fields -- Geometry of Shimura Varieties of Hodge Type over Finite Fields -- Lectures on Zeta Functions over Finite Fields -- De Rham Cohomology of Varieties over Fields of Positive Characteristic -- Homomorphisms of Abelian Varieties over Finite Fields -- Author Index.