The first 3 images are a Waxing Gibbous (Gibbous from the Latin word meaning "a hump or "bulging") Moon taken roughly 9 to 11 days after new moon. While the phases are changing from new moon to full moon it is waxing, when it is changing from full moon to new moon it is waning. The dark flat areas are called maria, meaning "seas" (pronounced "MAR ee uh"; singular, mare, pronounced
Galileo discovered that the moon had large flat and cratered areas, when he first viewed it through his small telescope in 1609.
The maria areas of the moon, were once cratered as the rest of it was, but were filled in by volcanic material -lava- that flowed from beneath its surface, more than 3 billion years ago. The craters you see now are from impacts since then.
Top image is of the southern highlands region.The large crater at lower center is Clavius, the smaller distinct crater above is Tycho.
The smaller Mare Crisium is to the far upper right, at the very top center of the image is Mare Serenitatis, at center is Mare Tranqullitatis to its lower right is Mare Fencunditatis.
At bottom left you will see the rayed crater Copernicus, above that is Mare Imbruim, and to its right is Mare Serenitatis, below that is Mare Tranquillitatis. The rays extending from craters are material ejected from meteorite impacts and over millions of years, will darken to match the surrounding surface, the most prominate of these are the crater Tycho. In the 2nd image you can just make out one of its rays extending to the north east.