Adeptus Astra Telepathica
The Adeptus Astra Telepathica is one of the most important organisations within the Imperium of Man. They are responsible for the training of nearly all psykers in the Imperium, except the Navigators and the Emperor-mulch of the Astronomican. Because of their overlapping field of expertise, they often work alongside the latter of those institutes. Because of the organisation's importance, the Master of the Adeptus Astra Telepathica is a permanent member of the High Lords of Terra.
Overview
The Adeptus Astra Telepathica consists of two separate bodies: the League of Blackships and the Scholastia Psykana. These are respectively responsible for the acquisition and training of Psykers.
The League of Blackships is the fleet of the Adeptus. It is a very large fleet that continuously visits every world in the Imperium every century or so to gather the tithes of Psykers of the worlds they visit. They are equipped with psi-shielded cargo holds that prevents their cargo's escape, at the cost of being very traumatizing to both the cargo itself and the crew, so only the strongest of mind can crew these vessles. It should be noted that these vessels are not to be confused with the Inquisitorial Black Ships, special Strike Cruisers that are, as the name suggests, completely black and unilluminated and serve as an intimidating extension of the Inquisitor's (and by extend, the Emperor's) will.
When the Blackships drop their cargo they are sorted into power and insanity: the least useful get a one-way trip to the Golden Throne, while the others are kept for training. Young children are a favorite because they are the easiest to train and indoctrinate. After five years of basic training (given they survive of course) they become Primary Psykers and are evaluated. A vast majority of them become Astropaths, while others (depending on potential, dedication, intellect and physical abilities) can become Primaris Psykers or Inquisitors, and the truly remarkable might attain the rank of Librarian or even that of Grey Knight.
Astropaths
Astropaths (a contraction of "astro-telepaths") are the email service of the Imperium. Since sending ships and physical objects through the warp is a dangerous and uncertain undertaking at best, the Astropaths are vital to the continued existence of the Imperium. They can telepathically send messages and even simple images through the warp to another target. At longer distances it becomes nearly impossible to send information accurately to another target: for this reason Astropathic Choirs were created. Beacons for the Astropaths, these are located on major worlds and starships where a number of Astropaths gather to form a Choir. These Astropathic Relays are meant to augment the abilities of Astropaths while shielding them from the horrors of the warp.
When their training is complete, Astropaths are brought before the Emperor 100 at a time to engage in a ritual called Soul Binding to help protect them from daemons. They all kneel before the Emperor who proceeds to reshape their very minds so they become true Astropaths. This ritual goes on for several hours during which the Astropaths experience great pain, their eyes and potentially more senses burn out, some are possessed by Daemons and others just go insane. Those who survive and retain their sanity are then inducted into the Astropaths and are given their traditional green robes.