Some wizards, instead of learning magic, learn the realms of psionics. They still must do book practice in order to not lose it all.
with the use of psionics, the wizard can cast spells from their mind, enhance them in certain ways and can use telepathy.

Mind magic

you encase your mind in a wellspring of psionic energy. This energy is represented by your Psionic Energy dice, which are each a d4. You have a number of these dice equal to twice your proficiency bonus, and they fuel various psionic powers you have, which are detailed below.

Some of your powers expend the Psionic Energy die they use, as specified in a power’s description, and you can’t use a power if it requires you to use a die when your dice are all expended. You regain all your expended Psionic Energy dice when you finish a long rest. In addition, as a bonus action, you can regain one expended Psionic Energy die, but you can’t do so again until you finish a short or long rest.

The powers below use your Psionic Energy dice.

Psionic casting. You expend one of your psionic die. You can then cast a prepared spell equal to the total rolled  + your intelligence modifier using a spellslot without using verbal and/or somatic components. you must still have the material for the spell if it requires it. If you have no spellslots for that spell level or it's been expended, you must cast a spell at the highest level spell slot available to you.

Telepathy. You expend a psionic die. You can talk to someone telepathically over a number of feet equal to the psionic die + intelligence modifier *10.

Mind barrier

At level 6, Your mind can protect yourself and others from harm. You have resistance to psychic damage.

Additionally, as a bonus action, You expend a psionic die. For 1 hour, you can give a number of creatures equal to the number rolled (including yourself) one of the following benefits:

Advantage on Wisdom, charisma and intelligence saves.
resistance to psychic damage.
Advantage on concentration saves.
A bonus to AC equal to your intelligence modifier.

you can use this once per long rest.

Mind gaze

At level 10, your mastery over psionic energy allows you to study creatures precisely. As an action, expend a psionic energy die. creatures have disadvantage on attacking you for a number of rounds equal to the psionic energy dice + your intelligence modifier. 

alternatively, as an reaction to seeing a creature make a intelligence, charisma or wisdom save, You reduce roll by an amount rolled on your psionic energy die.

Mystical prowess

At level 14, you have access to a mystical prowess. something the can define you as a mystical wizard. Pick one prowess, you gain their benefits.

Destroyer

Whilst you are apart of the prowess you have the following benifits:
you deal double damage to buildings and constructs.
You can score a critical hit with your spells on a 18-20
You can bypass resistance to slashing, bludgeoning and piercing damage.
You are proficient in martial weapons.

Indomitable

Whilst you are apart of the prowess you have the following benifits:
your Hit points increase by your level*2 , each time to level up it adds an extra +2 to your hit points.
you have proficiency in martial weapons and all armour.

Psion

Whilst you are apart of the prowess you have the following benifits:
You are immune to psychic damage.
you are immune to effects that allow people to detect thoughts or enter your mind. This also blocks telepathic communication by other creatures, unless you allow that creature to telepathically communicate.