You could check out Wikipedia: link
The references at the bottom of the article may also be helpful.
Many books mention about the pdf of the normal distribution, but where this pdf comes from? I would like to know the
theory behind the pdf. Can someone point me to the right direction.
Thank you in advance.
There is a derivation of it here http://courses.ncssm.edu/math/Talks/PDFS/normal.pdf
I think this one should be pretty good, but it's a bit fast (5 minutes). Normal distribution's probability density function derived in 5min - YouTube