In this thesis, we give an expanded account of trivolution on Banach algebras based on the work involutions and trivolutions in algebras related to second duals of group algebras by Filali, Monfared and Singh. Let $A$ be a Banach algebra. A trivolution on A is a non-zero conjugate-linear, anti homomorphism $\au$ on $A$, such that $$\au^?=\au .$$ The pair $(A,\au )$ is called a trivolutive algebra. We obtain several examples that they appear naturally on many Banach algebras. We show that every trivolutive algebra is an extension of an involutive algebra, such that $$A=I\\oplus B ,\\quad \au =\\rho p$$ in which $$p=\au ^?,\\quad B=p(A)=\au (A),\\quad I=\\ker p=\\ker \au,\\quad \\rho=\au\\vert_{B} .$$ We show that, a trivolution can have various
