As you play through the game, you'll happen upon several espers/summons. Some are found through the main storyline, and some are hidden and must be discovered. The hows and whys of this are in another thread. At the time of this (edited) post, JP has nine summons (Siren, Ifrit, Golem, Shiva, Ramuh, Diablo, Carbuncle, Odin, Titan), and Global has the first five. Each may be trained by giving it magicite shards of varying sizes and colours, and they gain levels from this. Each level gives the esper points to allocate to a colored table which may give it stats, abilities, spells, and more, which are given to the person who equips the summon. Magicite shards can be gained from events, purchased in some boxes in certain events, exploration maps, or (only in Japan for now) in a specific Vortex Dungeon. For now, each Summon has two ranks, 1* and 2*. You will start out with the 1*, and after maxing out the level (30), you can venture back to where you found the summon and fight a stronger version of it, which will upgrade your summon to 2*, also expanding the upgrades which it can each. For now, the maximum level of a 2* Summon is 40. The following pictures and text accompanying them are not my creations. They are also the upgraded 2* espers, so your starting espers may be lacking some of the outer plates.