In the first lecture I define Lie superalgebras, give some important examples: gl(m,n), osp(m,n), q(n) and p(n). Then I discuss

important properties of the category of finite-dimensional representations with reductive even part, stress the fact that the category is not semisimple, discuss the typical simple modules and formulate a weak version of BGG reciprocity. I would like also to explain the connection with algebraic supergroups if time permits.

In the second lecture I would like to concentrate on an example of one superalgebra, maybe gl(m,n) or q(n) and give overview of character formula and Kazhdan--Lusztig polynomials as well as classification of blocks.