What probability distribution represents the maximum of multiple of the same normal distribution?

Question

Given a normal distribution $N(\mu,\sigma^2)$, if we define a new distribution $M_n$ based on the maximum of $n$ random samples from the normal distribution $N$, what formula represents $M_n$. I'm certain the increasing the value of $n$ will continue to increase both $M$'s mean as well as decrease its variance, with diminishing returns for both, I'm also pretty certain that all $M_n$ will be normal distributions, but I remain unsure about how to model the distribution of the $M$'s.