Tilting Theory

"Tilting theory arises as a universal method for constructing equivalences between categories. Originally introduced in the context of module categories over finite dimensional algebras, tilting theory is now considered an essential tool in the study of many areas of mathematics, including finite and algebraic group theory, commutative and non-commutative algebraic geometry, and algebraic topology."
(From the Introduction to the Handbook of Tilting Theory, 2007).
 
The following survey will restrict to a narrow part of tilting theory: the original use of tilting modules over finite-dimensional hereditary algebras in order to define the class of tilted algebras.
 
This report is based on the work of a large number of mathematicians from various countries; a short account will be inserted dealing with the relationship to Padua.