Perverse Sheaves

For X a complex algebraic variety, the derived category D_cb(X) can be obtained starting from two natural, but quite different, abelian categories, namely the category C(X) of constructible sheaves on X and the category Perv(X) of perverse sheaves on X. The optimal way to understand this reality is the formalism of t-structures, to be introduced in the first section. The second section is devoted to the main properties of perverse sheaves and to a detailed description of germs of such sheaves in dimensions 0 and 1. The third section is a trip into the realm of D-module theory, trying to describe the dictionary behind the famous Riemann-Hilbert correspondence. Intersection cohomology, one of the sources of the perverse sheaves (maybe even their birth-place), is briefly discussed in the final section.