Ultima III: Exodus/Moongates

The greatest transport are the hidden Moon Gates. Passing through a Moon Gate when it is active will teleport your Party to another location. Access to many glens of the old knowledge are restricted by the Moon Gates. No creature of the Dark can ever break through the wards that protect them. The coming and going of the Moon Gates is somehow related to the twin Moons, Trammel and Felucca, that grace the sky. The success of your quest may well hinge on you solving the ancient mystery of the Moon Gates.

Understanding Moon Gates
At the top of the screen, the phases of the twin moons, Trammel and Felucca, are represented by numerals as follows:

The phase of the left moon dictates the location where you may find a Moon Gate currently open and awaiting utilization by your party. The phase of the right moon dictates the destination that you will end up in when you pass through the Moon Gate. The right moon changes phases three times for every one phase change of the left moon. This means every Moon Gate will lead to three particular destinations. In a few select cases, it is possible for the phases of the moons to be identical (New Moon, Gibbous waxing, Full Moon, and Crescent waning). During those moments, stepping into a Moon Gate will not transport you anywhere.

Moon gates timetables
Moon Gates are a from of transportation. You can think of them as similar to train stations or airports. As such, it can be easier to understand how to travel if the "timetable" of each "moon station" is displayed separately.

In the NES port, the "numbers" representing moon phases are replaced by actual moon icons. Note that they are mirrored with respect to the Earth's Moon. This is one of many hints throughout the series that suggests that the kingdom of Lord British is in the Southern hemisphere of its planet.

Mainland
Three moon gates (out of eight) can be accessed from Sosaria mainland. The one on Snake dungeon island ("Sol" in the NES) can be easily reached with a ship.

These three moongates send the party to two more destinations: the landlocked valley and Fire island.

On a return trip, they can be reached from three origins: Devil Guard valley, as well as the aforementioned landlocked valley and Fire island.

Landlocked valley & Devil Guard
The landlocked valley can be considered as a hub: there is nothing of interest, but the moon gates there allow to reach other areas. Most notably, both moon gates are linked to and from the valley of Devil Guard.

On the way back from Devil Guard, the party can skip the landlocked valley and travel straight to the Sosarian mainland.

Fire island & dungeon of Time
The moon gate on Fire Island allows to see Exodus Castle, but the party cannot reach it (unless you cheat using a glitch). This location can be considered as a hub: there is nothing of interest, but it allows to reach other areas. Most notably, the moon gate is linked to and from the valley of the dungeon of Time.

The party's quest to explore the dungeon of Time ("cave of Moon" in the NES) can start from the island of Dungeon Snake ("cave of Sol" in the NES). The moon phases of interest are all odd numbers: 1, 5, 7.