  This text has two parts; the first is the essentially unmodified text of the
1973-74 seminar of M. Lejeune-Jalabert and B. Teissier on integral dependence
in complex analytic geometry with J-J. Risler's appendix on the Lojasiewicz
exponents in the real analytic framework. The second part consists of seven
complements written in 2007 surveying recent results directly connected to the
content of the seminar. The main results of the first part concern the
asymptotic order function with respect to an ideal and in particular its
connection with the Lojasiewicz exponent. Another aspect concerns the
finiteness properties of the graded algebra associated with the filtration by
the asymptotic order function.
