do stuff. alot of stuff. all of the stuff. like, in every combination you can think of. hundreds of times each. (it sounds funny but that pretty much is the jist of it: play as a hunter and get thousands of scout rifle kills, play as a titan and get abjillion PVP kills, etc. just look at your grimoire cards and check on the bar graphs, it'll tell ya what you need)

Highest I have seen is 3675. Mine is 3415. You raise it fast by getting the dead ghosts, kills with all three kinds of characters in PVE and PVP. You complete public events and raids. You play [u]every crucible variant[/u] at least 50 times (unsure of how many to max). You single out VIP patrols. Killing 35 Skolas gives a hefty amount of grimoire score, in addition to all nine other POE bosses (unless I miscounted). There may be other things, but these are what many players are missing. Good Luck on reaching a high score Edit: Using all of the weapon types is also something that most players need to work on Note: Contrary to common assertion, exotic weapons DO NOT give grimoire score One more thing: If you have never seen Petra Venj In the tower, you will never reach max grimoire (unless she comes back)