Knowledge is power. An old idiom, but you have learned firsthand just how true it is. Your patron is a master of arcane knowledge, an archmage of peerless skilL such as Elminster or Merlin. They have taken a more direct hand in your growth, teaching you the basics of studying the arcane arts, which you use to bolster your own eldritch abilities.

Expanded Spell List

The Archmage lets you choose from an expanded list of spells when you learn a warlock spell. The following spells are added to the warlock spell list for you.

The Archmage Expanded Spells

Spell Level	Spells
1st	magic missile, shield
2nd	alter self, scorching ray
3rd	fireball, haste
4th	polymorph, otiluke's resilient sphere
5th	animate objects, bigby's hand

Bonus Cantrip

Your dabbling in the arcane arts has granted you a basic understanding of minor magical effects. You learn the prestidigitation cantrip. It counts as a warlock cantrip for you, but it doesn't count against your number of can trips known

Arcane Initiate

At 1st Level you have learned the basics of arcane study. You can add your Charisma modifier to any Arcana checks, rather than your Intelligence.

Also at 1st Level you have learned the methods of preparing spells from your patron. After finishing a Long Rest, you may prepare one spell from the Warlock spell list. A spell you choose must be of a level no higher than what's shown in the table's Slot Level column for your level

Review your notes

Beginning at 6th Level you learn the ability to replace your prepared spell with another. Over the course of a Short Rest, you may replace your prepared spell with another spell from the Warlock list. You may not do so again until you finish a Long Rest.

Photographic Memory

Starting at 10th Level you have developed the ability to reproduce a spell just by watching another person cast it. When another creature you can see casts a spell of a level which you can cast, you may use your reaction to make an Arcana check with a DC of 10 + the spell's level. 

On a success, you may memorize the spell to cast it yourself later. After memorizing a spell you may cast it once as a Warlock spell and the method of casting it fades from your mind immediately after. You may memorize only one spell at a time in this way, and you forget any spell you've memorized after a Long Rest.

Empty their minds

Starting at 14th level you have learned to rip knowledge out of your enemies' minds. You can cast feeblemind After you cast the spell with this feature, you can't do so again until you finish a long rest.