In this seminar I will give an introduction to the arithmetic of Calabi-Yau 3-folds.  The main quantities of interest are the numbers of points of the manifold considered as a manifold over finite fields.  I will be concerned with the computation of these numbers and their dependence on the complex structure parameters.  As we will see, these numbers are given by expressions which involve the periods of the manifold. I will discuss the form of zeta function of the Dwork pencil of quintic 3-folds and, time permitting, we will see what happens at singularities and speculate about what mirror symmetry has to say about the form of the zeta function.