References
Losing the modules:
Bernstein, Gelfand, Ponomarev. Uspeki Mat.Nauk 28 (1973)
Auslander, Platzek, Reiten. Trans.Amer.Math.Soc. 250 (1979)
Brenner, Butler. Spriner LNM 832 (1980)
Happel, Ringel. Trans.Amer.Math.Soc. 274(1982)
Papers by many mathematicians. See Handbook of Tilting Theory (2007).
Recovering the modules:
Several papers by Fomin and Zelevinsky.
Buan, Marsh, Reineke, Todorov, Reiten. Advances Math.
Buan, Marsh, Reiten. Trans.Amer.Math.Soc.
Keller.
Zhu.
Assem, Brüstle, Schiffler.
Keller, Reiten.
General Survey:
Ringel. Appendix to: Handbook of Tilting Theory (2007)