Hedge Wizard

A student of hard knocks as much as scholarly pursuits, hedge wizards are often self-taught, and take less orthodox methods of studying their spellcraft. They are less interested in tradition than they are in practicality. Some are radical prodigies that attempt to blend together different schools of magic, or reject the notion of the classical schools of magic altogether. Others are persistent arcanists that never received a formal education from a master or institution, improvising together any scraps of spellwork they can find into surprisingly effective spellbooks. Admittedly, the personalized jumble of their script often borders on unreadable to others, and at times, themselves.

Self Sufficient

You gain proficiency with light armor, one skill of your choice, and one tool or kit of your choice.

Unorthodox Spellcraft

When you add spells to your spellbook upon leveling up in this class, you can  make any of them spells from any class list and treat them as wizard spells. You can also scribe spells into your spellbook using scrolls and such from any class spell list, but doing so costs twice as much gold as normal.

Efficient Formulae

Starting at 6th level, you can cast a spell at one level higher than the spell slot expended, as long as you are holding your spellbook in one hand. You can use this feature a number of times equal to your proficiency modifier. You regain all uses of this feature after a long rest.

Resume Spell

Beginning at 10th level, you can recast a concentration spell that you had stopped concentrating on or lost concentration on before the end of it's duration without consuming a spell slot. The duration of the spell is shortened by the amount of time it was active during the first casting. You can only use this feature to resume a spell once per casting. You can only resume a spell that you stopped concentrating on less than a minute ago.

Arcane Improvization

Starting at 14th level, whenever you cast a spell of 1st level or higher that targets at least one creature, you effect a single targeted creature in one of the following ways:

If the spell made a successful attack against the creature or the creature failed a save as part of the spell, you can knock the creature prone, or push it up to 15 feet towards or away from you.

You can allow the creature to spend it's reaction to move up to it's speed.

You can increase the creature's AC by 2 until the end of your next turn.