The students which attends a mage's college are divided into ranks, based upon both the amount of time they've spent at a school, and the amount of mastery they show over their chosen form of magic. Though many seek it, few wizards are ever skilled enough to archive the rank of journeymage. One step below the ranks of those who serve as professors in such colleges a journeymage has shown a talent for magical research, and an incredible knowledge of the arcane arts as a whole.   Many journeymages are willing to remain at this rank, spending their time on further research and traveling to new cities to offer their services to those in need. Others instead choose to wander from place to place, seeking out new forms of magic and new arcane knowledge, hoping to progress far enough in their studies to eventually be granted the rank of archmage. 

Arcane Savant

Beginning when you select this school at 2nd level, when you copy a spell into your spell book, you may choose to double the amount of gold it takes in order to half the amount of time necessary, or vice-versa.

Collegiate Knowledge

Beginning at 2nd level, you gain proficiency in the Arcana skill. If you are already proficient, you can instead add double your proficiency bonus to all Intelligence (Arcana) checks you make. 

Balance of Spells

Also starting at 2nd level, you've learned to use the lingering magic on an enemy during a battle to enhance the effects of your own spells. When you hit a creature with a spell attack, it has disadvantage on the first saving throw it makes before the end of your next turn to avoid the effect of a spell you cast. Additionally, when a creature fails a saving throw against a spell you cast, you have advantage on the first spell attack roll you make targeting it before the end of your next turn. 

Arcane Skill

Starting at 6th level, you take the knowledge of study you gained during your time at the academy, and use it to perfectly memorize a single spell down to the details. Choose one 1st level wizard spell in your spell book. You always have this spell prepared, it doesn't count against the number of spells you have prepared, and you cast it once at 1st level without expanding a spell slot. When you do so, you can't do so again until you finish a short or long rest. .

If you want to cast the spell at a higher level, you must expand a spell slot at normal. At 12th level, you also choose one 2nd-level wizard spell in your spell book, gaining the same effects for the chosen spell. 

Perfect Balance

Beginning at 10th level, the remnant magic of your spells provides a powerful anchor for further effects. Once per long rest, when you hit a creature with a spell attack, the next time it makes a saving throw to avoid the effect of a spell you cast you can choose to have it automatically fail the saving throw. Additionally, when a creature fails a saving throw against a spell you cast, the next time you make a spell attack targeting it, you can choose to have the attack automatically hit. 

You must finish a long rest before you can use this feature again.

Academy Archmage

At 14th level, your studies have led you to the knowledge that magical energy can neither be created nor destroyed, only transferred. When you cast a spell of 1st level or higher, you can choose to automatically recover an expended spell slot of one level lower than the spell slot expended. If you cast the spell using a spell slot of 1st level, you instead regain a number of hit points equal to 1d4 + your spellcasting modifier.  You can use this feature once per long rest.