Well, MAX4466 is not a microphone, but a microphone preamplifier by Maxim. You must mean one of those microphone modules that are offered together with the amplifier in makershops etc, right?
There are many projects on the net that deal with this topic, e.g. this one. Most of them use a different MCU platform like e.g. Arduino, but with a little coding it should be quite easy to port it to STM32, which then offers way more performance than a small 8-bit MCU.