You gain proficiency in Arcana and Investigation

You have learned to regain some of your magical energy by studying your spellbook. Once per day when you finish a short rest, you can choose expended spell slots to recover. The spell slots can have a combined level that is equal to or less than half your wizard level (rounded up), and none of the slots can be 6th level or higher.

For example, if you're a 4th-level wizard, you can recover up to two levels worth of spell slots.

You can recover either a 2nd-level spell slot or two 1st-level spell slots.

You can prepare a number of spells equal to your Intelligence Modifier + your Level. Choose from the following list:
Cantrips:
Prestidigitation
Firebolt
Mage Hand
Message

1st Level:
Alarm
Detect Magic
Identify
Mage Armour
Shield
Sleep

2nd Level:
Alter Self
Enlarge/Reduce
Hold Person
Invisibility
Locate Object

3rd Level:
Fireball
Counterspell
Sending

Focusing on the manipulation of time, those who follow the Chronurgy tradition learn to alter the pace of reality to their liking. Using the ramping of anticipatory dunamis energy, these mages can bend the flow of time as adroitly as a skilled musician plays an instrument, lending themselves and their allies an advantage in the blink of an eye.

You can magically exert limited control over the flow of time around a creature. As a reaction, after you or a creature you can see within 30 feet of you makes an attack roll, an ability check, or a saving throw, you can force the creature to reroll. You make this decision after you see whether the roll succeeds or fails. The target must use the result of the second roll.

You can use this ability twice, and you regain any expended uses when you finish a long rest.

You can add your Intelligence modifier to your initiative rolls.

You learn to move things with your mind, granting you the following benefits:

Increase your Intelligence by 1, to a maximum of 20.

You learn the mage hand cantrip. You can cast it without verbal or somatic components, and you can make the spectral hand invisible. If you already know this spell, its range increases by 30 feet when you cast it. Its spellcasting ability is the ability increased by this feat.

As a bonus action, you can try to telekinetically shove one creature you can see within 30 feet of you. When you do so, the target must succeed on a Strength saving throw (DC 8 + your proficiency bonus + the ability modifier of the score increased by this feat) or be moved 5 feet toward you or away from you. A creature can willingly fail this save.

As an action, you can magically force a Large or smaller creature you can see within 60 feet of you to make a Constitution saving throw against your spell save DC. Unless the saving throw is a success, the creature is encased in a field of magical energy until the end of your next turn or until the creature takes any damage. While encased in this way, the creature is incapacitated and has a speed of 0.

You can use this feature a number of times equal to your Intelligence modifier (a minimum of once). You regain all expended uses when you finish a long rest.

Though others must often endure extensive interviews and significant fees to gain access to even the most common archives in your library, you have free and easy access to the majority of the library, though it might also have repositories of lore that are too valuable, magical, or secret to permit anyone immediate access.

You have a working knowledge of your cloister's personnel and bureaucracy, and you know how to navigate those connections with some ease.

Additionally, you are likely to gain preferential treatment at other libraries across the Realms, as professional courtesy to a fellow scholar.

You gain proficiency in History and Religion

You can read, speak and write Sylvan and Primordial.

Accustomed to life underground, you have superior vision in dark and dim conditions. You can see in dim light within 60 feet of you as if it were bright light, and in darkness as if it were dim light. You can't discern color in darkness, only shades of gray.

You have advantage on all Intelligence, Wisdom, and Charisma saving throws against magic.

You know the minor illusion cantrip. Intelligence is your spellcasting ability for it.

Through sounds and gestures, you can communicate simple ideas with Small or smaller beasts. Forest gnomes love animals and often keep squirrels, badgers, rabbits, moles, woodpeckers, and other creatures as beloved pets.

You can speak, read, and write Common and Gnomish.