This is the rework of the Wizard class, to represent magic and spellcasters more akin to the Elder Scrolls games. If you do not like the changes you can still use the vanilla Wizard, but I advise you to try this instead.
The Base features of the Wizard do not change, like Hitpoints, proficiencies etc. The main changes are the changes to spellcasting. It is strongly advised to use the Spell point variant rule presented in the DMG. I will treat the spell point variant as base for this conversion.
Cantrips: Cantrips do not change for the most part. The only change is that a wizard can choose to replace any and all of his cantrips in a place of study, such as a wizard's tower, the Arcane University, the College of Winterhold, etc. Replacing cantrips takes a week of study.
Spellbook: Spellbooks are completely removed from the game. The Mage remembers all his spells once he learned them, and can cast them any time, given he has spellpoints. The spells known are not limited in any way, but the wizard's money and time. Learning and creating spells is very expensive and time consuming process.
Preparing and casting spells: Spells do not need to be prepared to cast them. The Mage uses his Magicka (spellpoints) to cast any of the spells he knows.The Mage has no limitations on spellschools, he can learn any of the spells from any of the spellschools.
Spellcasting ability: A Mage can choose either his Intelligence or Wisdom(Willpower) as his spellcasting ability.
Alternatively the Mage can use Wisdom(Willpower) for his Spell save DC and Intelligence for his Spell attack modifier.
Ritual casting: Ritual casting does not exist (normally) in the Elder Scrolls games. More about rituals you can read about HERE.
Learning spells: A Mage is not limited how many spells he can learn, but he cannot learn spells that are too high in level for him to cast. Learning new spells usually cost a high amount of septims or a dangerous quest for the spell tome. Learning a spell takes hours of experimentaiton and spending spell points. A Mage must spend hours equal to the level of the spell, and 2 times the spellpoints required to cast the spell normally. Learning a 3rd level spell for example requires 3 hours of experimentation and 10 magicka (spellpoints).
Arcane Traditions: The arcane traditions will be posted on the blog in a separate entry.