In this thesis, we give an expanded account of closed ideals of Banach algebras based on the work “characterization of closed ideals with bounded approximate identities in commutative Banach algebras, complemented suaces of the group Von Neumann algebras and applications “by Lau and Ulger (2014) . We firstly define a number of fundamental terms such as: ideals, minimal ideals, commutative radical Banach algebras, quotient Banach algebras, approximate identity, modular ideal modular unit, invariant suace and invariant projection.