There are several methods of Fast Travel in Aeternum. There is currently no "group" fast travel (minus perhaps the automatic teleports to Expeditions, Outpost Rush, Corrupted Invasion, and War), but there are several options for single-player travel.
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Sanctuaries[]
After having visited a Sanctuary (Settlement, Outpost or Spirit Shrine) for the first time, you can use it for fast traveling to other sanctuaries. Players need to pay Azoth each time they fast travel. The farther a player travels and the more they are carrying at the time, the more Azoth it will require to teleport to their new location. Faction bonuses can reduce this cost.
Inn[]
If checked into an Inn (by entering an Inn and checking in), you can fast travel to it for free from anywhere in the world once every 60 minutes.
Housing[]
If you own a House, you can fast travel to it for free from anywhere in the world every 2 to 4 hours (depending on house tier). You can spend 10-50 Azoth (depending on the remaining cooldown) to remove that cooldown as often as you'd like. You can have up to 3 houses, which do not share a cooldown, and can be reset separately.
Roads[]
While it is not traditional "fast" travel, players receive a 10% movement speed bonus while on roads for longer than 3 seconds. The movement bonus will be cancelled if a player engages in combat in any way such as dodging, blocking, attacking, or being hit with a debuff.