A hyperbolic manifold is a quotient of hyperbolic space H
^n by a discrete group of isometries. In particular, an arithmetic hyperbolic manifold is a quotient of H
^n by a group which is in some sense arithmetic. For example, taking the quotient of H
^2 by an action of SL_2(Z
) yields more or less the (level 1) modular curve, which is a beloved object of number theorists around the world. Starting from the beginning, I will try to explain some of the rich structure of these arithmetic hyperbolic manifolds which make them particularly nice to study.