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I have been learning intersection homology and perverse sheaves in the following way. I started by reading the first $7$ chapters of Kirwan and Woolf's book http://www.amazon.com/Introduction-...

Let $X$ be a complex algebraic variety with an action of a connected algebraic group $G$. The forgetful functor from the category of $G$-equivariant perverse sheaves on $X$ to the category of perverse ...

The notion of cs-stratification of a topological space is apparently due to Siebenmann, see also the paper by N. Habegger and L. Saper in the paper "Intersection cohomology of cs-spaces and Zeeman's ...

There is a proper map $f: X \rightarrow Y$ of projective varieties. The Decomposition Theorem of Beilinson–Bernstein–Deligne-Gabber states that $$Rf∗IC_X  \cong \oplus_a IC_{\bar{Y_a}}(L_a)[shifts]$...