Spells Rank/Mark up

TL; DR version
Acquire Spell XP to obtain Rank ups, which unlock Augmentations and Passives, and at each 6th Rank you earn a Mark, which improves the Spell's Passives, but locks some Augmentations that you have to unlock again with more Ranks.

How they appear to the player
The Rank and Mark of each Spell can be found in the Spellbook, under the Spells, where the XP bar is. It is written in the form "X.Y", where X is the Spell's Mark, and Y is the Spell's Rank.

How to Rank up
Each Spell earn XP when used in a Loadout, in varying amounts depending on its positionning in the Loadout (the leftmost Spell earns 100% XP, and it decreases all the way to the right, down to 5% for the rightmost Spell). Each Rank has an XP requirement, and then the Spell must be tapped in the Spellbook when it has been met, to succesfully apply the Rank up. It is also worth noting that Spells no longer gain XP when they hit their XP requirement, which means that it is impossible to "overflow" to the next Rank. As such, offline play (already earning only 1/24th XP) is a lot less efficient to gain Ranks, since the player is not there to "confirm" the Rank up, which wastes XP.

Once Band of Perpetuation is unlocked at the Academy, it is possible to earn XP towards the next level even when the spell is waiting for Rank up, but at a reduced rate - 5% of normal XP rate for each level in Band of Perpetuation.

Why do I want to Rank up?
To unlock Augmentations and Passives! At Mark 1, each Rank unlocks a row, which boosts the Spell. The main difference between the two is that Augmentations only affect their own Spells, and as such the Spell has to be equipped for it to take effect, while Passives can affect other Spells, and grant their benefits even when they are not in the Loadout.

How to Mark up
At X.5, the Spell still gains XP, but this time, it's for a Mark up. When "confirmed", the Rank is reset to 0, and Augmentations are locked to some extent, determined by the Mark the Spell is at. At Mark 2, the first Augmentation stays unlocked, with Mark 3, the first and second stay available, and so on until it reaches Mark 6, where Marks no longer lock anything. Each Mark up also increases the Spell's Damage by +5% (additive to itself), so Mark 2 grant x1.05, Mark 3 gives x1.10, etc.

ALSO, the Spell's Passives will progressively get more powerful. Since the Spell continues to gain Ranks, it should unlock something at each Rank, right? Well, it's much better than that. Since Passives don't get locked, when the player reaches its "unlock Rank", that Passive gets boosted by the Mark 1 Passive's effect, multiplied by 1.2 for each Mark over 1. I'll put some math in here to clarify. Let's pretend that the 1.1 Passive of a Spell says "+100% Damage". At 2.1, the effect would become 100%, plus 100%*1.2, since it is Mark 2, totalling +220% Damage. At 3.1, it would take that 220%, add up 100%*1.2*1.2, which makes 144%, and it would become +366% Damage, and the pattern continues. But, Cooldown Rates are a bit more complicated than that... Each subsequent Mark still stacks with the previous ones, but the multiplier is 0.95 instead of 1.2, up until Mark 41. Though, as TopCog said, "no one should be making it that far anytime soon!" (as of v1.0.10).

Last important thing to note: Augmentations are NOT amplified by Marks.

Experience
Experience requirement to rank up at each level.

note: you will get full Augmentations upon reaching rank 5. 9.0 - 7.67 b

9.1 - 9.80 b

9.2 - 12.5 b

9.3 - 15.9 b

9.4 - 20.3 b

9.5 - 25.7 b