Basic summons, known as Eidolon's, have returned to Final Fantasy IX. Both Eiko and Dagger are the only characters that can call upon these beasts for aid.
To learn a Eidolon, you need to obtain the right Jewel for it, then get the AP needed. While you have the Jewel equipped, you can summon the Eidolon, without having gained the total amount of AP. But if you un-equip the Jewel before learning it, you will no longer be able to call upon that Eidolon.
Also, the power of the Eidolon depends on the summoning scene. The full version causes more damage, whereas the short version does less damage. To get the full summon each time, you will need to learn the "Boost" ability. This is learned from a Pumice Piece at 190 AP with Dagger, and 150 AP with Eiko.

Dagger's Eidolons

Name/td> Shiva Attack Diamond Dust Jewel Opal AP 20 MP 24	Name Ifrit Attack Flames of hell Jewel Topaz AP 35 MP 26
Name Ramuh Attack Judgement Bolt Jewel Peridot AP 30 MP 22	Name Atomos Attack G-Force 199 Jewel Amethyst AP 30 MP 32
Name Odin Attack Zantetzuken Jewel Dark Matter AP 30 MP 28	Name Leviathan Attack Tsunami Jewel Aquamarine AP 40 MP 42
Name Bahamut Attack Mega Flare Jewel Garnet AP 80 MP 56	Name Ark Attack Eternal Darkness Jewel Pumice AP 100 MP 80

Name Carbuncle Attack Various Jewel Ruby AP 35 MP 24	Name Fenrir Attack Various Jewel Saphire AP 55 MP 30
Name Phoenix Attack Rebirth Flame Jewel Phoenix Pinion AP 40 MP 32	Name Madeen Attack Terra Homing Jewel Ribbon AP 120 MP 54
There are a total of 4 different actions for Carbuncle. The action depends on the Jewel equiped at the time. Jewel Name Spell Cast No Jewel Ruby Light Reflect Emerald Emerald Light Haste Moonstone Pearl Light Protect Diamond Diamond Light Vanish	Fenrir also has two different Attacks, depending on what item you have equiped. Item Name Damage No item Terrestrial Rage Earth Attack Maiden Prayer Millennial Decay Wind Attack

There is one other Eidolon in Final Fantasy IX worth mentioning. This Eidolon is known as Alexander. He cannot be summoned by Eiko or Dagger individually, but rather is summoned by both together. It only happens once in the game, and is completely story-related. It is also the last time we will see this awesome summon to date.

Though I got this video from Limewire, and loaded it to Myspace account, there is still credit that should be given toFinal Fantasy IPFOX. This seems to be where the video originated from.