  This lecture presents recent advances in the theory of errors propagation. We
first explain in which cases the propagation of errors may be performed with a
first order differential calculus or needs a second order differential
calculus. Then we point out the link between error propagation and the concept
of second order vector in differential geometry, emphasizing the existence of a
slight ambiguity concerning the bias operator. The third part in devoted to the
powerful framework of Dirichlet forms whose main feature is to apply easily to
infinite dimensional models including the Wiener space (giving an
interpretation of Malliavin calculus in terms of errors), the Poisson space and
the Monte Carlo space. In the fourth part we show how an error in the usual
mathematical sense, i.e. an approximate quantity, may yield a Dirichlet form
and we introduce the four bias operators. Eventually we connect the Dirichlet
form with statistics by identifying the square of field operator with the
inverse of the Fisher information matrix.
