The first quarter moon is halfway between new and full moon. Half of the moon is illuminated and it's a quarter of the way through it's orbit around the Earth.
It's rare to have 7 eclipses in a calendar year. It's less rare to have 7 eclipses in 365 days. There are 7 eclipses in 365 days 29 times in the 21st century!
A waxing gibbous moon is in the sky before it's dark and lights up the early evening. It's more than half lighted, but not quite full. It sets after midnight.
What are sky measurements - or distances - in the night sky? Here's what it means for objects to be several degrees (or arcminutes or arcseconds) apart.
The new moon generally can't be seen, except during a solar eclipse. The moon crosses the sky with the sun during the day, and its shadow side faces Earth.
It has long been a sport for skywatchers to spot the youngest moon after sunset, with the eye alone. What does it take to see a very young crescent moon?