Tilting theory is one of the main tools in the representation theory of algebras. It originated with the study of reflection functors. The first set of axioms for a tilting module is due to Brenner and Butler; the one generally accepted now is due to Happel and Ringel. The main idea of tilting theory is that when the representation theory of an algebra A is difficult to study directly, it may be convenient to replace A with another simpler algebra B and to reduce the problem on A to a problem on B. We then construct an A-module T, called a tilting module, which can be thought of as being close to the Morita progenerators such that, if B = End TA, then the categories mod A and mod B are reasonably close to each other (but generally not equivalent). As will be seen, the knowledge of one of these module categories implies the knowledge of two distinguished full subcategories of the other, which form a torsion pair and thus determine up to extensions the whole module category. Because this procedure can be seen as generalising Morita theory, it is reasonable to give special attention to the full subcategory Gen TA of all A-modules generated by T and to use the adjoint functors HomA(T, −) and −⊗BT to compare mod A and mod B.