  In order to understand the linearization problem around a leaf of a singular
foliation, we extend the familiar holonomy map from the case of regular
foliations to the case of singular foliations. To this aim we introduce the
notion of holonomy transformation. Unlike the regular case, holonomy
transformations can not be attached to classes of paths in the foliation, but
rather to elements of the holonomy groupoid of the singular foliation. This
assignment is injective.
  Holonomy transformations allow us to link the linearization problem with the
compactness of the isotropy group of the holonomy groupoid, as well as with the
linearization problem for proper Lie groupoids.
