From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity(AI) of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper,we give some lower bounds on the algebraic immunity of Boolean functions.The results are applied to give lower bounds on the AI of symmetric Boolean functions and rotation symmetric Boolean functions.Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value「n/2」are constructed. From the motivation of algebraic attacks on stream and block ciphers, the concept of algebraic immunity (AI) of a Boolean function was introduced and studied extensively. High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper, we give some lower bounds on the algebraic immunity of Boolean functions. The results are applied to give lower bounds on the AI ​​of symmetric Boolean functions and rotation symmetric Boolean functions. Set balanced rotation symmetric Boolean functions with their AI near the maximum possible value “n / 2” are constructed.