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The state of the apparent moon as it varies through the synodical month of about 29.5 days, which is how long it takes the moon to circle the earth relative to the location of the sun.
The sequence is new moon, when sun and moon are precisely aligned (GHA of sun and moon near identical), then waxing crescent (letter D), then first quarter (half moon like filled in D, moon is some 90° east of the sun), then gibbous, then full (GHA of the moon about 180° from the sun), followed again by gibbous, then last quarter (half moon with filled in C, moon about 90° west of the sun), then crescent (letter C) and new moon again. The phase of the moon is sometimes presented as percentages. See note in the Resources Library (miscellaneous) on the French phrase "La lune est menteuse." See also the extended discussion of the moon in the Emergency Navigation book.
The age of the moon is the elapsed time in days since the last new moon. It is given on each of the daily pages of the nautical almanac. To get the phase from the age, divide 29.25 by the age, or vice versa.
In Table 3-3 of The Star Finder Book there is a table that relates the best time for moon sights based on the age of the moon.