Universalist Wizard

A wizard who forgoes specialization in one school in favor of learning universally applicable abilities. These wizards have learned to handle their spells most effectively. 

Arcane Prodigy

Beginning when you select this school at 2nd level, the gold and time you must spend to copy any spell into your spellbook is reduced by one quarter.

Hand of the Apprentice.

Beginning at 2nd level, you learn the Mage Hand Spell, and can use it to make the Attack Action with melee weapons. These attacks use your Intelligence in place of Strength or Dexterity. You do not count as threatening opportunity attacks with the Mage Hand unless you have made an attack that battle round. You can make attacks with this ability a number of time per day equal to your Intelligence modifier + your Proficiency bonus, after which you must take a long rest to regain them. 

You must have proficiency with the weapon used for this attack. Additionally, you gain proficiency with all simple weapons.

Metamagician

Starting at 6th level, you learn one meta magic ability from the list below. You may learn another one at level 12 and at level 18. You have a number of Metamagic points to spend on these equal to your proficiency bonus. You gain these points back on a long rest.

Metamagic Choice

Select one of the following at levels 6, 12, and 18.

Careful Spell. When you cast a spell that forces other creatures to make a saving throw, you can protect some of those creatures from the spell’s full force. To do so, you spend 1 Metamagic point and choose a number of those creatures up to your Intelligence modifier (minimum of one creature). A chosen creature automatically succeeds on its saving throw against the spell.

Quickened Spell. When you cast a spell that has a casting time of 1 action, you can spend 2 Metamagic points to change the casting time to 1 bonus action for this casting.

Subtle Spell. When you cast a spell, you can spend 1 Metamagic point to cast it without any somatic or verbal components.

Extended Spell. When you cast a spell that has a duration of 1 minute or longer, you can spend 1 Metamagic point to double its duration, to a maximum duration of 24 hours.

Distant Spell. When you cast a spell that has a range of 5 feet or greater, you can spend 1 sorcery point to double the range of the spell.

When you cast a spell that has a range of touch, you can spend 1 Metamagic point to make the range of the spell 30 feet.

Full Spellbook

Beginning at 10th level, you learn an additional number of first level spells, from any spell list, equal to your Int modifier.

Arcane Threadweaver

Starting at 14th level, you can attempt to recover you spells after casting them. Using your reaction after you cast a spell, you take damage equal to twice the spell level, and then make a concentration check with a DC equal to 10 + the spell's level; on a success you regain the spell slot.