  This is not standard in the sense that we understand a Springer map to be a
collapsing of homogeneous bundles. Apart from that we use mostly techniques
from Chriss and Ginzbergs book but we work in the equivariant derived category
of Bernstein and Lunts. We define Steinberg algebras as (equivariant)
Borel-Moore homology algebras of the associated Steinberg varieties. The data
of the BBD-decomposition theorem applied to the Springer map give a
parametrization of projective graded and simple graded modules over the
Steinberg algebra. Also, the projective graded modules are equivalent to a
category of shifts of perverse sheaves. This has as a consequence for example
the Springer correspondence. We call classical Springer Theory what is usually
considered as Springer Theory. The main results are parametrizations of simple
modules of different types of Hecke algebras. Our second main example is
quiver-graded Springer theory (due to Lusztig), here the Steinberg algebras are
the quiver Hecke algebras. We also explain Lusztig's and Khovanov-Lauda's
monoidal categorification of the negative half of the quantum group using the
categories of shifts of perverse sheaves and projective graded modules over the
quiver Hecke algebra respectively.
