Order of the Tutor

A spirit of magic stands at your side to guide you to greatness, hoping that you will be able to carry on where they left off. Perhaps they are a famous wizard who died before they could finish their master work spell, maybe its your mother in law who was a mage and is constantly critiquing the way you cast spells. Who the Companion is, is up to you.

Otherworldly Supporter

When you take this subclass at 2 level a mage who has passed on, takes interest in your potential. You gain a Spirit Companion.
The Spirit Companion is a invisible medium sized undead, it has a movement speed equal to yours. Also if the spirit speaks only you can hear it. The spirit can perform simple tasks that a human servant could do, such as fetching things, cleaning, mending, folding clothes, lighting fires, serving food, and pouring wine. Once you give the command, the spirit performs the task to the best of its ability until it completes the task it then returns to you. Your spirit is intangible and can see into the ethereal plane up to 30ft. It cant go further than 60 foot away from you.

Your Spirit Companion can't directly effect a battle, it has no hit points but can not be destroyed. you can use your bonus action to command the spirit. it can take the Help, Search, or Use an object actions.

A Master's Guidance

A Masters Guidance

At 2nd level your Spirit Companion's skill in magic allows you to learn spells faster. The gold and time you must spend to copy a spell into your spell book are halved. Also when you take a long rest roll a d20 on a roll of your level or less you can choose a new spell from your Companion's spell book. (this book knows all wizard spells from levels 1 to 5) The spell chosen must be from a level your are able to cast, the cost and time required to copy the spell into your spell book is the same as if copying from a scroll. You can't use this feature again until you finish copying the spell into your spell book.

Companions Experience

At 6th level your Spirit Companion is able to tell what level a spell is being cast at, If you choose to use your reaction to cast the Counterspell magic then the DM must inform you of what level the spell is cast before you expend your spell slot.

When casting a spell as a ritual you can cast it in half the time mentioned on the spell.

As an action, you can hear and see using the Companion's senses, instead of your own, until your concentration ends (as if concentrating on a spell). Whenever you cast a wizard spell on your turn, you can cast it as if you were in the Companion's space, instead of your own, using its senses. You can do so a number of times per day equal to your proficiency bonus, and you regain all expended uses when you finish a long rest.

Spell Master

At 10th level with guidance from your Spirit Companion You may choose a 1st level spell and a 2nd level spell. You always have these spells prepared, they don’t count against the number of spells you have prepared, and you can cast each of them once per long rest without expending a spell slot. If you want to cast either spell at a higher level, you must expend a spell slot as normal. At 18th level when you gain Spell Mastery these two spells become your default choice, You can then select an additional 1st level spell with the ritual tag, you can cast this spell instantly without expending a spell slot.

By spending 8 hours in study, you can exchange one or all of the spells you chose, for different spells of the same levels.

1st level spell selection

The first level spell choice for your Spell Master Feature.

2nd level spell choice

2nd level spell choice

ritual spell

ritual spell choice

Surpassing Expectations

At 14th level While your Spirit Companion is within 5 ft of you you gain the following abilities; 

1: You can cast Spells without need for the verbal and somatic components.
2: When you cast a spell that deals damage you can roll, treat any damage rolls of 2 or lower as 3. 
3: When you cast a spell that has a saving throw, you can give a single target disadvantage by expending an additional spell slot of 1st level or higher. 

Also if your Spirit Companion shares the same space as you, then you have advantage on saving throws against spells and other magical effects. You also have resistance against the damage of spells.