Coven of the Hedge

Those of the hedge are frowned upon by scholars, by fellow wizards who had the chance to attend college for their craft. Fellow scholars see them as the dropouts, the lazy, those who could not make the prestigious cut- but the Hedge Wizard is just as passionate, if not more passionate than their fellow wizards. They simply have more unorthodox methods compared to those taught in colleges- 

Picked up from study. 

Picked up from hands-on experiences. 

Picked up from trail and error.

After all, the hedge wizard is, if nothing else- a self-taught skill-monkey.

For some, this is not a choice- but they make due, using magic and knowledge practically- using it, more akin to how one would an occupation. Doing little favors and labor to earn gold- as they continue to study, continue to push what they can do- experimenting, to find what works- and what explodes upon attempt. 

And while the more prestigious sneer, an accomplished hedge wizard knows more than they ever will.

Student of The World

You've learned magic through practical experience- it is only natural you picked up some skills or, odd, but resourceful spells along the way.

As of second level, you have proficiency in one tool of your choice and two of the following skills - History, Nature, Religion, Medicine, Survival, or Animal Handling.
You also gain the cantrip mending and one of the following- Druidcraft, Predesignation, or Thaumaturgy.

Cantrip Choice (Druidcraft)

Choose between Druidcraft, Predesignation, or Thaumaturgy. You chose Druidcraft. 

Cantrip Choice (Predesignation)

Choose between Druidcraft, Predesignation, or Thaumaturgy. You chose Predesignation. 

Cantrip Choice (Thaumaturgy)

Choose between Druidcraft, Predesignation, or Thaumaturgy. You chose Thaumaturgy. 

Revisionist

As of second level, you have become a more flexible arcane caster. You may take a short rest and forgo healing with hit dice, although you still gain the other benefits of a short rest. You may instead choose to replace a number of prepared spells, equal to your proficiency bonus, with another known spell. 

Ecyclopedia-Based Spellbook

As of sixth level, your experience, and thusly- your knowledge, has become quite vast. Even your spellbook shows this, filled with clusters upon clusters of notes you've gained over the years- each remembered. Whenever you make an intelligence-based skill check that you are proficient in, you may spend a first-level spell slot to double your proficiency bonus for that roll. However, this must be done before you roll.

Improvised Casting

Hedge wizards often must make due with what they have. You are no different. Whenever you cast a spell with a material component with monetary cost, you can expend half the gold needed to cast the spell or use a material component half as expensive.
But sometimes, making due isn't enough. You also may, once per long rest, use a bonus action to change one prepared spell with another. 

Jack of All, Master of None

You've observed not only wizardry, but other forms of magic through other casters- you've even borrowed some of their methods. As of fourteenth level, pick one seventh-level or lower spell that is not from the wizard spell list. You may now cast this spell as normal, however, it is not affected by your Revisionist and Improvised Casting abilities. You must also use the spellcasting ability of the class you took it from for this spell.