Electret mics contain a built-in JFET that requires mic bias to be applied via a resistor, usually 2-10V via a 2k2 - 10K resistor. Very rough numbers.
What you have posted is power amplifier with a gain of 10 (R5 and R6 form a voltage divider for negative feedback). Q1 and Q2 provide a higher current push-pull output than the 5532 can on its own, so it can drive small speakers.
What is the application? Is this mic being used with a 'line-in' on equipment? or are you actually driving a speaker? Either way I would recommend googling a 'low noise preamp' to get your mic signal up to line level, then a power/speaker amplifier if you wish to drive speakers with it.
I have seen a few transistor preamps with very low noise, and there are single transistor preamps that will give you plenty of gain but perhaps not overly quiet. Opamp preamps can be very low noise but with any preamp, the bias for the electret mic provides a path from the power supply, to the amplifier input and so any noise on that line gets amplified. I have no idea if you are a hobbyist, or what 'skill' level you are at (not that its something that can be measured!) but assuming you're just starting out, I would suggest looking for single transistor amplifiers, googling how they work, and playing about with component values. If you just want a 'quality electret preamp' google has many examples!
The NE5532 is a very capable opamp for audio but if its for a preamp (driving line level input) you won't need the transistors on the output.