The first view of the Aether Foundation is in the opening cutscene where it shows Lillie running from various Aether Foundation employees and Ultra Recon Squad Members after taking Cosmog. It ends with Cosmog creating a portal for it and Lillie to escape.

Location: Diglett's Tunnel

Your next active encounter with the Aether Foundation is in Diglett's Tunnel. When travelling through there, you will encounter two employees who will greet you. They will inform you that Team Skull had been riling up Pokémon in the area and that Team Skull often interfere with Pokémon.

Location: Memorial Hill

When you get to Memorial Hill later in the game, you will encounter an Aether Foundation employee and their boss arguing with Team Skull over a Slowpoke. The Aether admin requests that you fight in his stead to stop Team Skull from taking the tail from the Slowpoke. If you do, they suggest going the Hano Grand Resort hotel so you can talk to him.

Location: Hano Grand Resort

When you reach the Hano Grand Resort, you will meet the Aether admin you helped in Memorial Hill. He will introduce himself as Faba and will offer an invite for you to go visit the Aether Paradise, a special island created by the Aether Foundation in the middle of the Alola Region. You, along with Hau, then go to the boat to go to the Aether Paradise!

Location: Aether Paradise

When you get on the boat to the Aether Paradise, Faba will show you around. He will note that there is a jamming signal in the Aether Paradise so that nobody can use Poké Balls and capture the Pokémon in the area. They want to create a safe haven for Pokémon where people such as Team Skull cannot get them. Faba then introduces you to Wicke, another of the Branch Admins, who takes you and Hau up to the special Conservation Area.

In the Conservation Area, you then meet the character Lusamine who explains how she is creating the Aether Paradise to look after all Pokémon. However, while talking, an Ultra Wormhole appears and an Ultra Beast comes out of it, leaving you to have to battle it. It gets a Defense boost

Ultra Beast

???

Level 27

Attacks: Clear Smog Psywave Headbutt Venoshock

Hold Item: No Item

When defeated, the Ultra Recon Squad will soon appear and will discuss the fact that they are helping the Aether Foundation with their knowledge of Ultra Beasts in exchange for help with the issues caused by the Pokémon Necrozma. Lusamine then instructs Wicke to send you to Ula'Ula Island

Location: Ula'ula Meadow

As you go through Ula'ula Meadow to confront Team Skull, you will bump into Faba who will question why you're there. He will note he's taking the initiative to check up on all the Pokémon and that he's been thinking of dealing with the Necrozma issue on their own and asks if you think his acts are worthy of being a president.

Location: Aether Paradise

The next encounter with the Aether Paradise comes much later in the game after Lillie has been kidnapped by Team Skull. Gladion makes the connection and states that Lillie has been taken to the Aether Paradise and that you, he, and Hau must go there to rescue Lillie and stop their plan.

When there, the Aether Foundation employees will now challenge you to battles as they have been given orders to stop anyone from going through. As you progress, you will learn that you can't go to the basement so you have to go up and try to get the key from Branch Chief Faba. Eventually, you go to the Secret Labs in the basement to get the information about Cosmog being an Ultra Beast, with the help of Wicke.

Aether Branch Chief Faba	Claydol	Bruxish	Hypno
Battle Type Items	Level 44	Level 44	Level 45
	Attacks: Earth Power Extrasensory Ancient Power Grass Knot	Attacks: Aqua Jet Crunch Psychic Fangs Waterfall	Attacks: Psychic Hypnosis Focus Blast Nightmare
	Hold Item: No Item	Hold Item: No Item	Hold Item: No Item

Location: Aether Paradise

As you battle through, you discover that Aether Foundation and Team Skull have in fact been working together, with Guzma there in order to help Lusamine achieve her goal. Once Guzma has been defeated, you, Gladion, and Hau are able to get into the main room where Lusamine is, with Lillie and Cosmog. Lusamine intends to use Cosmog's energy to open an Ultra Wormhole to travel to Ultra Megalopolis in order to stop Necrozma herself so she can save Pokémon. Wormholes begin to open all across the Alola Region.

Following this, Lusamine then challenges you to a battle.

Aether President Lusamine	Clefable	Lilligant	Lopunny	Milotic	Bewear
Battle Type Items	Level 47	Level 47	Level 47	Level 47	Level 47
	Attacks: Moonblast Charm Psychic Hyper Voice	Attacks: Petal Dance Teeter Dance Stun Spore	Attacks: Dizzy Punch Thunder Punch Ice Punch Fire Punch	Attacks: Hydro Pump Icy Wind Flail Dragon Pulse	Attacks: Zen Headbutt Drain Punch Take Down Dual Chop
	Hold Item: No Item	Hold Item: No Item	Hold Item: No Item	Hold Item: No Item	Hold Item: No Item

After defeating Lusamine, the wormhole will start to close and Lusamine goes in, with Guzma quickly following. After the wormhole is closed, it seems Cosmog has evolved into Cosmoem. The Ultra Recon Squad are angry that Lusamine left to save Necrozma just to fulfil her desires rather than to actually help them while Lillie is eager to find her mother and save her from Necrozma but Galdion & Wicke mention that perhaps the power of Solgaleo/Lunala can awaken Cosmoem and create a wormhole to get Lusamine back. Lillie changes her look and Gladion wishes you well on your journey by giving you the Moon Flute/Sun Flute.

Location: Altar of the Sunne/Moone

Once you have got the other flute from Exeggutor Island and made it to the Altar of the Sunne/Altar of the Moone, you awaken the powers of Solgaleo/Lunala and have Cosmoem evolve into it. As it goes to create an Ultra Wormhole, one opens already and Guzma & Lusamine fall out of it, followed quickly by Necrozma as their plan failed. Necrozma appears and takes over Solgaleo & Lunala, requiring you to go through the Ultra Wormhole to stop it.

After defeating Necrozma, Lillie and Lusamine will return to the Aether Foundation.

Location: Poni Grove

You'll briefly encounter Wicke of the Aether Foundation after the Ultra Recon Squad have called on you to help out with some Ultra Beasts causing havoc in Poni Grove. She will meet you in Ancient Poni Path and will offer you a Type: Null from Gladion, as Gladion has left to go to Kanto. She'll also give you Beast Balls that were developed with the Ultra Recon Squad and let you know that you can buy them in the Aether Paradise, where they are working with the Ultra Recon Squad to research Ultra Beasts.

Location: Aether Foundation

Shortly after Sophocles informs you of Festival Plaza being overrun, your mother will show a trick of her having taught Meowth how to turn on the TV. It will cut to a press conference where Lusamine and Wicke are explaining what happened during the Poni Island incident when Necrozma appeared. However, the press conference gets interrupted by an Ultra Wormhole opening and a Rocket Grunt running towards Lusamine, with Giovanni not far behind.

Lillie will run into your house shocked by this and say she is heading to the Aether Paradise to go check if her mother is alright. Follow her and you'll get there to see that the building has changed to a castle. As you go to go inside, Faba will stop you and say there's no stopping Giovanni's plans as they can save even more Pokémon. He will challenge you and Lillie to a Multi Battle.

Aether Branch Chief Faba	Claydol	Bruxish	Hypno
Battle Type Items	Level 63	Level 63	Level 63
	Attacks: Earth Power Extrasensory Ancient Power Grass Knot	Attacks: Aqua Jet Crunch Psychic Fangs Waterfall	Attacks: Psychic Hypnosis Focus Blast Dream Eater
	Hold Item: No Item	Hold Item: No Item	Hold Item: No Item

Location: Aether Foundation

After stopping Team Rainbow Rocket, things return to normal in the Aether Foundation, with Lusamine in charge, Wicke helping you and giving you the 55 Big Nuggets she found, and general protection of Pokémon. However, due to his involvement in Team Rainbow Rocket, Faba is demoted from Branch Chief to Intern. Faba can be found and will battle you, insisting he is changed but still having aspirations of being President

Aether Foundation Faba	Claydol	Bruxish	Raichu	Alakazam	Hypno
Battle Type Items	Level 63	Level 63	Level 63	Level 63	Level 63
	Attacks: Earth Power Extrasensory Ancient Power Grass Knot	Attacks: Aqua Jet Crunch Psychic Fangs Screech	Attacks: Psychic Thunderbolt Quick Attack Nuzzle	Attacks: Psychic Psyshock Disable Dazzling Gleam	Attacks: Psychic Hypnosis Focus Blast Dream Eater
	Hold Item: No Item	Hold Item: No Item	Hold Item: No Item	Hold Item: No Item	Hold Item: No Item