  In this paper we consider so-called Google matrices and show that all
eigenvalues ($\lambda$) of them have a fundamental property $|\lambda|\leq 1$.
The stochastic eigenvector corresponding to $\lambda=1$ called the PageRank
vector plays a central role in the Google's software. We study it in detail and
present some important problems.
  The purpose of the paper is to make {\bf the heart of Google} clearer for
undergraduates.
