The Academy is where all your Research happens. It personally is my top priority behind Keep to upgrade as each level gives access to more and more Technologies that you can research thus making your troops stronger, speeding up construction and research times, speeding up resource production and gathering, and even increasing hospital capacity and rally size! Do not neglect your academy or you will regret it later. Every bit of gold spent here pays for itself tenfold in a very short amount of time!
Building Specific General:Eulji Mundeok
The Duty Officer for the Academy provides a boost to your Research Speed based off of the General's Politics and Leadership Stats. This boost is not insignificant and can knocks days off of a Research timer when doing big Techs in the later game. Because of this, you want to make sure to always assign the best possible General as the Duty Officer before starting a Research project.
Skill Book Shop:
The Skill Book Shop operates much like the Black Market. It presents 6 different skill books from level 1 (3k Gems) to level 3 (8k Gems) that you can purchase. Like the Black Market, the Skill Book Shop refreshes at regular intervals so that you can check for fresh books several times a day. Also like the Black Market, there is a Reroll (Refresh) button that gives you 6 new Skill Books in the shop for just 50 Gems.
In all reality you only want to buy the Level 1 Skill Books to use to get your 3 Skills set on your Generals. After you have the Skills locked in place (if you don't have Level 4 copies of those Skills) you can still buy the Level 1 Books and Disassemble them for Skill Book Pages that you can then reassemble 10 of for a Level 4 Skill Book Chest which will award you a random Level 4 Skill Book.