Most of monks learn how to use ki to improve their body and mind, but some dive deeper in the more mystical root of this energy. The “way of the mystical arts” concentrate on the mastery of ki to use and improve their spell casting.
Those monastic spell caster learn the secret of the ki and magic to improve their understanding of the world. They master the school of transmutation and abjuration, channeling their ki to use spell to alter matter and mystical energies. Some of those individual take interest into more secret and deeper magical ability.  

Spellcasting

When you reach 3rd level, you gain proficiency in Arcana, and you augment your martial prowess with the ability to cast spells.
Thanks to your ki, you can ignore material non costly component for spell casting.

Additionally, when you gain a level in this class, you can choose one of the "Way of the mystical arts" spells you know and replace it with another spell from the way of the mystical arts spell list, which also must be of a level for which you have spell slots.

You learn the cantrip Prestidigitation and one other cantrip from the school of transmutation or abjuration in the wizard spells list. You gain an additional cantrip if you have at least 10 in Intelligence.

This monk has spell slots to cast his spell.

Monk level	Cantrip known (with intelligence below 10)	Spells knows	1st	2nd	3rd	4th
3	Prestidigitation + 1	4	2	-	-	-
4	Prestidigitation + 1	4	3	-	-	-
5	Prestidigitation + 1	5	3	-	-	-
6	Prestidigitation + 1	5	3	-	-	-
7	Prestidigitation + 1	6	4	2	-	-
8	Prestidigitation + 1	6	4	2	-	-
9	Prestidigitation + 1	7	4	2	-	-
10	Prestidigitation + 2	8	4	3	-	-
11	Prestidigitation + 2	8	4	3	-	-
12	Prestidigitation + 2	9	4	3	-	-
13	Prestidigitation + 2	10	4	3	2	-
14	Prestidigitation + 2	10	4	3	2	-
15	Prestidigitation + 2	10	4	3	2	-
16	Prestidigitation + 2	11	4	3	3	-
17	Prestidigitation + 2	12	4	3	3	-
18	Prestidigitation + 2	12	4	3	3	-
19	Prestidigitation + 2	13	4	3	3	1
20	Prestidigitation + 2	14	4	3	3	1

 

For your spells and cantrips known, you can choose spells form the Transmutation and Abjuration schools of magic in the wizard spells lists.
The only exception is the spell “Magic missile”, who can be chosen even if it is an evocation spell.

You regain all expended spell slots when you finish a long rest.

Even if you cast spells from the wizard spells list, your monastery taught you how to meditate on the mystical force who rule the world and use them with respect. So, your spellcasting ability is Wisdom. You use your Wisdom whenever a spell refers to your spellcasting ability. In addition, you use your Wisdom modifier when setting the saving throw DC for a way of the mystical arts spell you cast and when making an attack roll with one.

Spell save DC = 8 + your proficiency bonus + your Wisdom modifier

Spell attack modifier = your proficiency bonus + your Wisdom modifier

Arcane meditation

At level 3, When your recover your ki point with a short rest, you can choose to immediately spend these ki point to regain expended spells slots.

If you spend one ki point, you regain one expended 1 level spells slots.
At level 7 or higher, if you can spend two ki point, to regain one expended 2 level spells slots.
At level 13 or higher, if you can spend three ki point, to regain one expended 3 level spells slots.
And finally, at level 19 or higher, if you can spend four ki point, to regain one expended 4 level spells slots.

You can spend as many ki point as you want or can.

Mystical martial artist

At level 6, When you use your action to cast a spell, you can spend 1 ki point to perform an unarmed strike as part of this action.  You can't benefit from your extra attack feature when you do that, but you still can use your bonus action to make another unarmed strike or a furry of blow.

You can perform this ability only once per turn. However, if the spell affects multiple targets, or attack the same target multiple time, this ability cost 4 ki points instead.

Ki and mysticism

At level 11, you can ignore your spell’s verbal component, unless the spell as only verbal component. You also can use your reaction and spend 1 ki point to gain one of these temporary and situational magical effects:

-When you are target by a spell that required a saving throw, you gain an advantage on saving throws against that spell

-When you cast a spell that required a saving throw from one target you hit with an unarmed strike on your turn or on the previous one, you impose a disadvantage one this saving throw.

-When you concentrate on a spell and you have to make a saving throw to maintain concentration, you automatically success.

-When you take magical damage, you gain magic resistance against that attack.

-When you perform your first unarmed strike on your turn, you can change the damage type to be “Force damage” instead of “Bludgeoning damage”. This change affects all the unarmed strikes you will made on this turn.

Secret of the arcane

Your monastery has taken interest into other form of magic. At level 17, with your discipline, you start to learn your monastery’s secret only known by masters. You can choose one of these options:

-Master of spellcasting: Choose four spells from any classes, including spell from the wizard spell list. A spell you choose must be of a level you can cast, as shown on the Way of the mystical arts table, or a cantrip. The chosen spells count as way of the mystical arts spells for you and are included in the number in the Spells Known column of this table.

-Master of cantrips: Choose two spells from any classes, including spell from the wizard spell list. A spell you choose must be of a level you can cast, as shown on the Way of the mystical arts table, or a cantrip, but you have to choose at least one cantrip. The chosen spells count as way of the mystical arts spells for you and are included in the number in the Spells Known column of this table.
This option doubles your number of cantrip known, so you can have a lot of cantrip now.

-Eldritch truth: Choose two spells from any classes, including spell from the wizard spell list. A spell you choose must be of a level you can cast, as shown on the Way of the mystical arts table, or a cantrip. The chosen spells count as way of the mystical arts spells for you and are included in the number in the Spells Known column of this table.
You also choose an eldritch invocation. However, you can only choose an eldritch evocation with no prerequisite or spell slot needed. Level prerequisites are ignored.

-Master of eldritch powers: You can choose two eldritch invocations. However, you can only choose an eldritch evocation with no prerequisite or spell slot needed. Level prerequisites are ignored.