School of Spell Mastery

Spell Mastery is an arcane tradition fixated on understanding the underlying mechanics of magic. It is the most academic of all arcane traditions. The promise of uncovering new knowledge or proving (or discrediting) a theory of magic is usually required to rouse its practitioners from their laboratories, academies, and archives to pursue a life of adventure. 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.

Wizardry Lore

Starting at 2nd level, you become a compendium of knowledge on a vast array of topics. Your proficiency bonus is doubled for any ability check you make that uses the Arcana, History, Nature, or Religion skill if you are proficient in that skill.

In addition, your analytical abilities are so wellhoned that your initiative in combat can be driven by mental agility, rather than physical agility. When you roll initiative, it is either an Intelligence check or a Dexterity check for you (your choice).

Adaptive Arcanery

Starting at 2nd level. With true comprehension on spells allow you to alter the nature of it at will. When you cast a spell with a spell slot and the spell deals acid, cold, fire, force, lightning, necrotic, radiant, 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). 

Augmented Arcanery

Beginning at 2nd level. As a bonus action, you can modify your spell you cast because of your knowledge of magic alteration. You have a number of mastery points to spend equal to half of your wizard level (round down), and you regain all expended uses when you finish a long rest.

Vigorous Cast (1 point). If you roll damage for the spell when you cast it, increase the damage against every target by 2d10 necrotic, radiant or force damage type of your choice. If the spell can deal damage on more than one turn, it deals this extra damage only on the turn you cast the spell.
Crafted Configuration (2 points). When you cast a spell with a spell slot and the spell requires a saving throw, you can change the saving throw from one ability score to another of your choice. 
Refined Spell (3 points). As a bonus action or reaction, you can increase or decrease one spell's DC by 2. This feature only apply to spells you know or have encoutered before.

Spell Withstanding

Starting at 6th level, even the simplest spell casting technique requires a deep understanding of how arcane energy can affect the world around us. This understanding allows you to alter your defenses to better deal with threats. After you finish a short or long rest you can switch any saving throws with your Intelligence saving throws. This apply whenever you egage agianst spells or magic items. To do so, choose Strength, Dexterity, Constitution, Wisdom or Charisma. You use Intelligence saving throws in saves instead of using that ability saving throws, and vice versa. This effect can lasts until you finish your next short or long rest.

Also, you can use Intelligence modifier instead of Constitution modifier for checking your concentration of your spell.

Mastery of Magic

Starting at 10th level. Choose two classes from Bard, Cleric, Druid, Sorcerer and Warlock. You can call to mind the ability to cast one spell of your choice from two of chosen classes’ spell list you pick when you gain this feature. The spell must be of a level for which you have spell slots, you mustn’t have it prepared, and you follow the normal rules for casting it, including expending a spell slot. If the spell isn’t a wizard spell, it counts as a wizard spell when you cast it. The ability to cast the spell vanishes from your mind when you cast it or when the current turn ends.

You can use this feature once per long rest. When your reach to 15th level, you can choose an additional class's spell list.

Superior Incarnation

Beginning at 14th level. Through your devotion toward arcane study, you invoke secret knowledges of magic to provide you an infinite power for spell casting. Choose one of following choices. You can use this feature once and can use it again after you take a long rest.

Equivalent Exchange. When you take damage from spell you can halve that damage and cast that spell on your next turn as an action without expend spell slot. 

Crimson Incantation. You can cast a spell without component by take 1d12 necrotic damage per spell's level and your max hit points is reduced by the same amount. This effect lasts long until you take a long rest.

Beyond Intellectual. You can maintain two concentration spell at the same time and cast a spell that require an action as a bonus action.

Foul Influence. As a reaction, when other creature cast a spell you can treat that spell's DC as 10.