Telepathy is an Elven strategy, usually meshed with other strategies like Elvents or Gil-Galad Looping. It originated in Movie Block, but remains strong throughout the rest of the formats. Telepathy focuses on manipulating the top cards of the deck with tools like Gandalf, Manager of Wizards (7R37) and Back to the Light (18R6), then using your tailored top cards to win skirmishes with Forearmed (6U16) and similar cards}}.
Most versions of telepathy rely on the classic Gandalf, Manager of Wizards (7R37) and Forearmed (6U16) combo. Paired with a high-costing shadow like Sauron Besiegers and Sudden Strike, you can place a minion such as Sauron, The Lord of the Rings (9R+48) on top of your deck. Usually the starting fellowship in Movie Block consists of Glorfindel, Revealed in Wrath (9R+16) and Legolas, Archer of Mirkwood (5P121) so you can forego Forearmed (6U16) against Nazgul and keep your fellowship healed. Once you get to post-Shadows formats, however, the starting companions become more varied. With the rise of Gil-galad, High King of the Noldor (18R12), meshing telepathy with his token looping abilities became the standard telepathy deck. As a bonus, he can recur your Forearmed (6U16) at the cost of threats. As such, threat removal such as Golrfindel, Eldarin Lord or Into the West (7C23) is necessary. In addition, the powerful Elrond, Witness to History (12R17) can help to fuel Into the West (7C23) or even recur your Elven cards.
Building the Deck
For a strong Movie Block telepathy deck, you generally will want either Galadriel, Bearer of Wisdom (9R+14) or Frodo, Courteous Halfling (4R301) as your Ring-bearer. If you intend to play other Elven events other than Forearmed (6U16), it is beneficial to play Frodo and then start Galadriel, Lady Redeemed (10R11). You will also want to start Glorfindel, Revealed in Wrath (9R+16) with either Legolas or Arwen (Arwen, Echo of Luthien (10U5) is often played). Gandalf, Manager of Wizards (7R37) is a must, as there are no better tools to manipulate your deck. You will need four copies of Forearmed (6U16), as there are no real good recursion methods for them. If you play other events, using Círdan, The Shipwright (10R8) as a backup is a solid addition. Elf-song (1C39), Narya (3R34), or Sam, Son of Hamfast (1C311) are all viable burden removal options. Depending on your meta, playing counters to certain strategies like Southron Archery, Nazgul Corruption, or Corsairs can be beneficial, if you can find the space.
In formats such as Expanded and Standard, the archetype changes dramatically. Forearmed (6U16) and Gandalf, Manager of Wizards (7R37) are still keystones, but there are more options for the other cards. Galadriel, Bearer of Wisdom (9R+14) is usually the Ring-bearer, and you start Gamling, Defender of the Hornburg (11R147) to tutor Erkenbrand’s Horn to grab Celebring, Elven-smith (18R7) (which in turn grabs Galadriel's Silver Ewer (18R11)) and Woodhall Elf, Exile (18C17). Arwen is usually the other starting companion, either Arwen, She-Elf (15R11) or Arwen, Royal Maiden (19P6). Most cards from the Gil-Galad Looping strategy are incorporated, covering burden and condition removal, plus an infinite card draw loop. Círdan, The Shipwright (10R8) is rarely used, as you rely only on a few events, namely, Forearmed (6U16) and Attunement (12C16).
However, if you choose to mesh telepathy with Elvents, you often will take a different route. Most likely, you will start a similar fellowship, or you will play Elladan, Son of Elrond (14R2) and Elrohir, Son of Elrond (14R3). While you will probably still use Gil-galad, High King of the Noldor (18R12), you will probably not use his loopable ability. After that, you will pack your deck with Elven events, plus Gandalf and Círdan, The Shipwright (10R8).