Your training has focused more on the theory and study of magic than its practical use. Rather than specializing in a particular school of spells, you concentrate on the underlying mechanics of the incantations, gestures, and arcane ingredients required to cast them all. You are almost certainly connected to some kind of magical college or university; at the very least you studied with a wizard who trained many apprentices in a rigorous pedagogical approach.
Spellcasters of your tradition refer to themselves as savants, loremasters, or academicians, though more self-taught wizards may refer to your colleagues by the mocking nickname “Mages of the Ivory Tower.” Though they see you as isolated, aloof, or naïve, none can deny your mastery of spellcasting. Some members of your arcane tradition reciprocate by looking down upon non-academic arcane casters as provincial bumpkins, often referring to them as “hedge wizards.” Other academicians are eager to learn from and teach any wizard they meet, overwhelming such prejudices with their sheer enthusiasm for magical study.

Academic Education

At 2nd level when you choose this arcane tradition, you gain proficiency in the Arcana and History skills. You gain expertise with both skills, which means your proficiency bonus is doubled for any ability check you make with them. In addition, whenever you make an Intelligence check that does not include your proficiency bonus, you can add half your proficiency bonus, rounded down, to that roll.

Spellcasting Secrets

At 2nd level, you can alter a spell’s formula as you cast it, changing its effects. Choose two of the following damage types: acid, cold, fire, lightning, poison, necrotic, radiant, or thunder. When you use a spell slot to cast a spell that deals damage of one of the two types you chose, you can substitute that damage type with the other type you chose. When you reach 7th level, 13th level, and 17th level, you can choose additional damage types from the list above, substituting these types for each other as you wish when you use this feature. In addition, when you use a spell slot to cast a spell that requires a saving throw, you can change the saving throw from its normal ability score to your choice of Dexterity, Constitution, or Wisdom. Once you change a saving throw in this way, you can’t do so again until you finish a short or long rest.

Acid

You can substitute acid damage.

Cold

You can substitute cold damage.

Fire

You can substitute fire damage.

Lightning

You can substitute lightning damage.

Necrotic

You can substitute necrotic damage.

Poison

You can substitute poison damage.

Radiant

You can substitute radiant damage.

Thunder

You can substitute thunder damage.

Metamagic Scholar

At 6th level, your deep studies of spellcasting allow you to apply metamagic effects, similar to a sorcerer’s, to spells prepared from your spellbook. You expend additional spell slots to fuel these effects, allowing you to make the following alterations to your spells:

• When you cast a spell you have prepared, if that spell has a range of touch, or a range of 5 feet or greater, you can expend an additional spell slot to extend the range of that spell beyond its normal limit. If the spell has a range of touch, you make the range of the spell 30 feet. If it has a range of 5 feet or greater, you double the range of that spell.
• When you cast a spell you have prepared, if you roll damage for that spell during the same turn you cast it, you can expend an additional spell slot to add 2d8 to one damage roll of that spell against one target. If you wish, you can expend multiple spell slots in this way, increasing the damage against a different one of the spell's targets for each additional spell slot expended.
• When you cast a spell you have prepared, if that spell forces a creature to make a saving throw to resist its effects, you can expend an additional spell slot of 3rd-level or higher to give one target of the spell disadvantage on its first saving throw made against the spell.

Spellpool

At 10th level, when you prepare your spells each day, you can make use of a spellpool, a magical reservoir of spells that can be drawn upon by members of your wizardly guild or magical academy. To do so, you must purchase a special arcane focus, which can be of any type you wish, but for which the cost is 25 gp higher than normal. This arcane focus allows you (and only you) to access the spellpool from any distance. If you lose this arcane focus, you must replace it, for the same cost, at a place where you can contact other members of your organization. When accessing the spellpool, you attempt to prepare a spell that is not in your spellbook. To do so, you must use an action to check to see if the spell is available by rolling percentile dice. The chance of a particular spell being available is 60% plus your wizard level, minus 5% per level of the spell. You can even check to see if a spell not on the wizard spell list is available, but doing so decreases the chances of the spell being available by 25%. You cannot check for a spell if you do not have a spell of that spell’s same level or higher in your spellbook. If the spell is available, you may prepare it normally, even if it is not in your spellbook; if not, you cannot prepare that particular spell using this feature until the next time you finish a long rest, at which point you must check for this spell's availability again. There is no limit to the number of spells you can search for in this manner, but the maximum number of spells you can prepare with this feature at one time is equal to your proficiency bonus. For each spell you prepare with this feature, you must donate a spell of the same level or higher from your spellbook to the spellpool. A spell you donate is treated as if it were not in your spellbook at all until the next time you finish a long rest. A spell prepared using the spellpool returns to it the next time you finish a long rest, at which point you prepare your spells normally from your spellbook, unless you choose to use this feature again. Having successfully prepared a spell with this feature previously does not alter your chances of finding it available again.

Instant Preparation

At 14th level, you can use your Spellpool feature instantly in a time of need. As either an action or a bonus action (your choice each time you use this feature), you scour the spellpool for one particular spell, rolling to see if it is available as per the Spellpool feature. When you check the availability of a spell with this feature, you can roll the percentile dice twice and choose which of the two rolls to use. If the spell you sought is available, you instantly prepare that spell, swapping it for a spell of the same level or higher that you already have prepared, with the swapped spell being donated to the spellpool as normal. Otherwise, this feature works exactly like your Spellpool feature, allowing you to keep the spell prepared until the next time you finish a long rest. Once you use this feature to successfully prepare a spell, you cannot use it again until you finish a long rest.