To achieve this, you'll need to fill five more positions in your Library's staff, by asking your friends to come and work with you. To be specific, your Library already has 10 staff members, and you need 15 to upgrade. Once that's done, the upgrade process isn't complete just yet, as you can upgrade from Level 2 to Level 3 by gathering 10 more staff to work with you (specifically, going from 15 to 25 staff members in total). Finishing this task will see your Library not only take its final visual form as a larger, more grand building, but will also increase the total population allowed by the building to 700.
Altogether, these Library upgrades may only add 300 citizens to your total maximum population, but since they don't require you to ask for dozens of different building ingredients, I think it evens itself out. We'll make sure to let you know when more building upgrades are released for your city, so keep checking back.
Have you started the Library upgrades in your city? What do you think of them - do they upgrade the population stat high enough, or should we be given more room for citizens for the work we put into upgrading? Sound off in the comments.