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LED Brightnes STM32F3

So I have an assigment where I need to do the following:
- 10stages of brightnes (from lowest to highest)
- at each button press we change stage for 1
- first brightnes is going up, when reaches maximum is going down (does not jump to 0)
- button needs to be linked to timer, so timer does the counting and not the program

I'm totally new in electronics and in programming ARM. I know how to check for button press,how to toggle LED and where to set up PWM.

I know that LED brightnes needs to be controlled by PWM. What I don't know is how to corectly set up pulse,period of PWM and all that stuff about button click.
I would appricate any help.