You never need to simplify any type of algebra. It often helps people understand answers better and/or makes working with certain algebraic expressions easier in the future, but always remember that a simplified and unsimplified expression or algebra are both saying the same thing.
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To simplify a circuit you must first find a Boolean expression for the circuit and then apply Boolean algebra to take it down to the simplest form, to implement the fewest gates.
The prototypical Boolean algebra; i.e. the Boolean algebra defined over the Boolean domain, has two elements in it: 0 and 1. For more information about Boolean algebra, please refer to the related link below.
Most likely it is called BOOLEAN ALGEBRA I.
George Boole invented Boolean algebra.
One use of Boolean algebra is to minimize any function or logic gate.