Conrad Murray -- The Inmate with the Dragon Tattoo

Conrad Murray is CRUSHING his reading list behind bars ... finishing more than 60 books during his stint in captivity ... including "The Girl with the Dragon Tattoo" ... this according to his baby mama.

"Don't Worry" Murray's on-again, off-again GF Nicole Alvarez says she's been in constant contact with Connie since he was locked up in L.A. County Jail ... and says he's been desperately trying to keep his mind active.

"He's been doing a lot of reading ... he's able to transport himself to all these different places ... like Sweden or Paris or Afghanistan."

Alvarez says Murray has also started a virtual "university" behind bars ... educating other inmates in various subjects.