abstract: A multiarrangements is a natural generalization of hyperplane arrangements where we associate multiplicities to each yperplane. The aim of this talk is to give a generalization of some parts of the theory of critical points of simple arrangements to multiarrangements. The main object is the logarithmic ideal of a multiarrangement which characterizes the freeness of the multiarrangements similar to the simple case. We will also explain the geometry of the zero locus of this ideal and present a complex which turns to be free resolution in case of free multiarrangements.