  In the first part of my talk I will explain a solution to the extension of
Lie's problem on classification of "local continuous transformation groups of a
finite-dimensional manifold" to the case of supermanifolds. (More precisely,
the problem is to classify simple linearly compact Lie superalgebras, i.e.
toplogical Lie superalgebras whose underlying space is a topological product of
finite-dimensional vector spaces). In the second part I will explain how this
result is used in a classification of superconformal algebras. The list
consists of affine superalgebras and certain super extensions of the Virasoro
algebra. In the third part I will discuss representation theory of affine
superalgebras and its relation to "almost" modular forms. Furthermore, I will
explain how the quantum reduction of these representations leads to a unified
representation theory of super extensions of the Virasoro algebra. In the forth
part I will discuss representation theory of exceptional simple
infinite-dimensional linearly compact Lie superalgebras and will speculate on
its relation to the Standard Model.
