The remarks below are added in view of readers' observations, for which I am always very grateful, or they reflect my new insights in this area of Mathematics. The references in brackets correspond to the references in the book.

1. Luis Narváez Macarro has noticed that the construction of the perverse sheaf associated to a diagram on pp. 141-142 is wrong. For a correct construction in terms of real constructible sheaves we refer to the following sources.
   • [GGM1], pp. 7-14.
   • Philippe Maisonobe: Germes de D-modules à une variable et leurs solutions, in: Introduction à la théorie algébrique des système différentiels, Travaux en cours 34, Hermann, Paris, 1988.
   Related questions are discussed in:
   • Luis Narváez Macarro: Cycles évanescents et faisceaux pervers: cas des courbes planes irréductibles, Compositio Math. 65 (1988), 321-347.
   • Luis Narváez Macarro: Cycles évanescents et faisceaux pervers. II. Cas des courbes planes réductibles, London Math. Soc. Lecture Note Ser. 201 (1994), 285--323.
   • F. Gudiel and Luis Narváez Macarro: Explicit models for perverse sheaves, Rev. Mat. Iberoamer. 19 (2003), 425-454.
   • Philippe Maisonobe: Faiseaux pervers dont le support singulier est une courbe plane, Compositio Math.62(1987),215-261.
2. The use of local systems (and of the associated intersection cohomology sheaves) which are not of finite rank over the field of rational (or complex) numbers has produced very interesting results in topology, see for instance the following papers.
   • S. Cappell, J. Shaneson: Singular spaces, characteristic classes, and intersection homology, Annals of Math. 134 (1991), 325-374.
   • G. Friedman: Intersection Alexander polynomials, Topology (2004), 71-117.
   • L. Maxim: Intersection homology and Alexander modules of hypersurface complements, Ph.D. Thesis, Univ. of Pennsylvania (2004), math.AT/0409412. This paper is directly related to some results in Chapter 6 of our book, see my detailed remarks in Alexander invariants and transversality.
3. An important perverse sheaf associated to a holonomic D-module is the irregularity complex along a hypersurfaces, see
   • Z. Mebkhout: Le Théorème de positivité, le théorème de comparaison et le théorème d'existence de Riemann, in: Séminaires et Congrès 8, Soc. Math. France (2004). (downloadable from http://smf.emath.fr/.)
   In the same paper, Z. Mebkhout propose to call the perverse sheaves 'sheaves in the derived sense', arguing as follows against the use of the traditional terminology. " Nous ne souhaitons pas utiliser cette terminologie qui coupe net cette belle notion de ses racines."