Known as savants, followers of this tradition are a bookish lot who see beauty and mystery in the application of magic. The results of a spell are less interesting to them than the process that creates it. Some savants take a haughty attitude toward those who follow a tradition focused on a single school of magic, seeing them as provincial and lacking the sophistication needed to master true magic. Other savants are generous teachers, countering ignorance and deception with deep knowledge and good humor. 

Master of lore

Starting at 2nd level,Your proficiency bonus is doubled for 2 skills your choice from Arcana, History, Nature, or Religion skills if you are proficient in that skill, if not you can chose to gain proficiency instead, also you learn one cantrip of your choice. 

When you select this tradition at 2nd level, your knowledge of the arcane allows you to keep a larger number of spells prepared than other wizards. Allowing you to prepare a additional number of spells equal to your proficiency bonuns.

 Also your extensive knowledge of the arcane improves the rate at which you study new spells,  the time you must spend to copy a wizard spell into your spellbook is halved.

Arcane alteration

At 2nd level, you master the first in a series of arcane secrets uncovered by your extensive studies.

When you cast a spell with a spell slot and the spell deals acid, cold, fire,lightning, or thunder damage, you can substitute that damage type with one other type from that list (you can change only one damage type per casting of a spell). You replace one energy type for another by altering the spell’s formula as you cast it

The list expands to necrotic,radiant,physic,  and force at 10th level 

Arcane advancement

At 6th Level Your knowledge of the arcane also allows you to cast spells few other wizards can. You may choose two spells from any spell list they do not have to be from the same spell list. A spell you choose must be of a level you can prepare, as shown on the Wizard table, or a cantrip, though cantrips chosen this way do not count against the number of Cantrips Known on the Wizard table. Add the chosen spells to your spell book, which count as wizard spells for you. Other wizards cannot copy these spells into their spell books.

also because of your growing arcane ability when you use your arcane recovery you can regain a additional level of spells equal to your int modifier. (min of 1)

Archivist of the arcane

At 10th level, you can remember spells from your book with ease. You may now change your list of prepared spells when you finish a short or long rest.
you can copy any spells from spell scrolls that you find into your spellbook, even if these spells do not appear on the wizard spell list. Difficult although possible you may now expand your arcane ability to the furthest reaches of what thought possible, copying these spells don't come easy and cost double that of copying a wizard spell. (100gp and 4 hours per spell level) Once copied these spells count as Wizard spells and prepare them as normal. 

Arcane authority

At 14th level, Because of your constant research into the arcane and spells you have broken the limits you once knew. You may choose two more spells from any spell list and add them to your spellbook, also now every time you gain a level in the Wizard class (starting with 15th level), one of the spells that you add to your spellbook may come from any spell list, though you are free to learn two wizard spells if you prefer. Your spellcasting is now bounded only by your own interests and imagination. You have grown accustom to studying and copying spells of all types as such you can now copy any spell at normal cost.