Boolean algebra is the algebra of binary logic values 0 and 1. It defines basic operations like OR (+), AND (.*), and laws such as commutativity (A+B=B+A), distributivity (A(B+C)=(AB)+(AC)), idempotency (A+A=A), complement (A+A'=1), and De Morgan's laws (A+B)'=A'B'). Boolean algebra is used in logic design and digital circuitry to reduce complex logical expressions and optimize logic gate implementations.