  The usual crossed product construction which associates to the homeomorphism
$T$ of the locally compact space $X$ the C$^*$-algebra $C^*(X,T)$ is extended
to the case of a partial local homeomorphism $T$. For example, the
Cuntz-Krieger algebras are the C$^*$-algebras of the one-sided Markov shifts.
The generalizations of the Cuntz-Krieger algebras (graph algebras, algebras
$O_A$ where $A$ is an infinite matrix) which have been introduced recently can
also be described as C$^*$-algebras of Markov chains with countably many
states. This is useful to obtain such properties of these algebras as
nuclearity, simplicity or pure infiniteness. One also gives examples of strong
Morita equivalences arising from dynamical systems equivalences.
