I know there are some spells that allow different classes to control a beast to do something for them so one idea I brought up as a funny joke concept was having a Wizard Bartender that was controlling a bunch of Mimics and having them act as the furniture. Pay the mimics to use them as chairs and tables to eat and the Mimics would later use the coin to pay the Bartender for food. The mimics would act as security for the bar because if you started a fight in the bar the furniture would kick your ass and make you the next meal. 

With this in mind, an interesting idea came to mind when one of our group said they would DM the next campaign and said we could pretty much do anything, but I want to know if this specific element would actually work. Could a Wizard use some sort of control spell to make a book Mimic its pet and then use it as a spell book? When the Mimic is in its book form would you still be able to open it, read spells to prepare for the day, and add new spells into it? When it is in its Mimic form, Would it continue to act as a normal book Mimic or would it gain something unique as a result of having magic spells engraved on its insides by a Wizard? The idea is that I would have a Wizard that would have a book that, if you tried to steal it, the book would attack you. At the same token, if the Wizard ran out of spells, he could literally hit them with the book and the book would eat them. 

I'm thinking of something along the lines of the grim-war used in Harry Potter for the Magical Beasts class that Hagrid had everyone buy. 

How would I make this work if my DM would be willing to allow it should I find a random Mimic on the travels. 

This is a very homebrew idea. I dont think there is anything in the rules you can base this on. You will have to ask the DM.

Mimics in previous versions of D&D were more intelligent. Even in 5e, the entry under Cunning Hunters suggests that there are more intelligent Mimics, who also could be willing to trade safe passage for food.

I think it's plausible enough to even have the mimics cooperate without the use of magic.

It might have taken a while to find all the friendly intelligent mimics to 'furnish' a tavern/bar, but if your DM is willing to play along, go for it.

It may be borderline canon, but still viable in my understanding.

So having a mimic that could act as a spell book for a wizard would also be very homebrew then? Images indicate that when a mimic changes to its living form it has a mouth and tongue. So if it can hold its book form I could save spells in it. 

I know a lot of weapons have some sort of magical effect like ice or fire. This means there is some way to bind magic to the item. Could this work with a mimic book as well allowing me to bind one of the spells in the book to the mimic, and because the book is sentient could it technically cast the spell on its own? A gem placed in the book cover that adds 1 spell slot for a specific spell set at a certain level as an example? 

So if i bind the Shield spell to a 2nd lvl spell slot gem, if i'm getting hit by a spell that would beat my armor class I could encourage the book to use the spell to keep us both safe or the DM could claim the Mimic decided to use the spell to protect me. 

A mimic doesn't transform into an object, it just takes the appearance of it. 

The creature would look like a book, but still have internal organs and such, not pages to write on. 

A functioning mimic spellbook would be homebrew.

I could see that if you flavor it right it could *maybe* work, assuming the mimic is friendly. Like account256 said, mimics just look like those objects, but are still organic living things. That being said, I could see a mimic potentially having all the important organs towards the "bottom" of the book, and then having some thin flaps of skin that look kinda like the pages in the top half of the book. It would be like writing on flesh, but I'd say doable

The difficulty is making the mimic friendly to you with magic. I could be wrong, but I am not sure of any spell that permanently makes a monster friendly to you. You would either have to recast the spell at regular intervals (burning spell slots) or try to bribe the mimic like the bartending idea. If I were to homebrew it, I would simply treat the control spell similar to the teleportation circle spell, where if you cast it repeatedly over time, the effect becomes permanent. In this way, it could either be something your character works towards, or could be written off as something accomplished before the campaign started. 

FYI, I don't know if it's in 5e yet, but there was an old adventure involving an island full of Mimics. The island itself? Also a Mimic. A Mimic-furnished bar isn't that far-fetched.

As for a Mimic spellbook? No, that'd be 100% up to your DM as a homebrew. 

As a Homebrew idea, mimic familiar. I'd probably not have the mimic be my spell book, but it would be a great trap for anyone trying to steal/ destroy my book ;-)

As a Mimic takes the outward appearance of an object, and not its inside, I dont think this could work as you describe; however there is another option:

Tame a Mimic as a book, and have it hold a Spellshard (from Wayfinder's Guide) for you. The shard can function as a spellbook, and with the mimic holding it for you, it can look like you are using a book instead when using it, the mimic can protect it, and should the poor mimic ever be killed, the shard is still available.

Just dont forget rations for your mimic, nor a pen to carry the illusion.

I've gotta say... I really like this idea, although yeah... in the core rulebook there's no way to pull this off, but it would be really fun to homebrew. If I was going to justify it, you could have the Mimic pose as the Cover to the book, while the pages inside are still just normal.

Yeah you would need to homebrew this mimic to be a spellbook. Honestly it doesn't sound to far of a leap for a DM to make a mimic book and it would be fun to have as a "WTF is that" moment lol.