http://nssdc.gsfc.nasa.gov/planetary/planets/moonpage.html

The Moon's mass is about 1/80 of the Earth's, and its radius is about 1/4 of the Earth's (see figure below).  The Moon is one of the largest satellites in the solar system, and it is by far the largest satellite in the terrestrial planet group (only Mars and Earth have satellites in this group, and Mars' satellites are tiny).  the Moon is frequently classified as a terrestrial planet, and the Earth-Moon system is sometimes considered a double planet.

The Moon is in a spin-orbit resonance, which means that the ratio of its spin period to its orbital period is a simple ratio of whole numbers n:m

Actually, the Moon's specific resonance is 1:1, which is why we can only see one side from the Earth.

Click here to see how this resonance works: spin-orbit resonance

The Moon's surface is classified into highlands (heavily cratered) and maria (meaning "seas" -- not so heavily cratered).

Here are two links to images of the Moon:

Lunar Map Catalog

Apollo Panoramas

Here is a diagram (to scale) of the Moon's interior, comparing it with the Earth's:

The Moon is iron-poor!  The small iron core shown in the diagram comes from indirect evidence.

How do we know that the Moon has only a small core?

(1) The mean density of the Moon is 3.34 g/cm³, which is very close to that of uncompressed magnesium-silicate rocks.

(2) It is possible to check how much the Moon's density varies with depth, using a method related to the method used for the Earth, which makes use of the Earth's oblateness.  This method tells us that there is very little density variation inside the Moon.

(3) Solar wind carries solar magnetic field lines past the Moon.  The field lines would be caught by a conducting iron core in the Moon, since conducting iron acts like a plasma.  We see little evidence for this:

Results from the Apollo magnetometer experiment were more like (A) than (B).

Here are some images of the Apollo 16 magnetometer:

and deployed on the surface of the moon:

(4) Seismology -- Apollo astronauts placed a few seismographs on the Moon's nearside:

Recall that Potassium-40 ₁₉K⁴⁰ is an unstable isotope of potassium that decays in two ways.
Most of the decays form ₁₈Ar⁴⁰  (Z goes down by one), and the half-life for this process is 1.28 Gyr.  We can use this decay process as a clock.  Argon is too volatile to be chemically incorporated in rocks, so if we find argon-40 trapped in a rock, we can be pretty sure that it is the product of decay of potassium-40 that was originally in the rock.  So by measuring the amount of argon-40 relative to potassium-40, we can determine how many half-lives have elapsed since the rock was formed.  The age of a rock is the time that has elapsed since the rock became a closed system.  In practice, this means the time that has elapsed since the rock crystallized, cooled, and remained undisturbed by its environment.

Click here to see a little movie depicting the decay of radioactive potassium-40 (red) to volatile argon-40 (green), which is locked in a matrix of solid rock (blue).

Another important way that the Moon differs from Earth:
The highlands rocks (heavily cratered) are mostly plagioclase feldspar: a silicate mineral rich in refractory elements Ca and Al.  This indicates that this, the oldest part of the Moon, formed at very high temperatures.

The Moon is depleted in siderophile elements, not just iron.

A formerly fashionable model for the origin of the Moon, which explains much of this:
 giant impact on the early Earth:

After the collision, all the iron drains into the center of the Earth.  Very high temperatures are generated during the collision and its aftermath, which explains the Moon's depletion of volatile elements and compounds. 

But: a big problem with the impact theory is that the distribution of certain isotopes in the Moon is identical with the same distribution in the Earth.  These isotopes indicate that the Moon is just a refractory-enriched chunk of the early Earth, and that none of it came from elsewhere in the solar system.  You'd think that some of an impacting object would end up in the Moon, but there's no evidence for this.

At present (2014), planetary scientists are puzzled about how the Moon came to be.  An earlier theory by George Darwin (son of Charles) is coming back into fashion.  This theory  supposes that the early Earth was spinning so fast that it spun off a chunk that became the Moon.

The lunar highlands became saturation-cratered when the Moon finished accreting, about 3.8 Gyr ago.  Late volcanism flooded the mare basins.  The Moon ceased to be active by about 3.1 Gyr ago.  Radioactive heating, which maintains the Earth's activity at present, is not effective in the Moon.

Here is a diagram showing the difference between saturated cratering and unsaturated cratering:

The highlands are saturated at all scales.  The maria are smooth-looking at large scales, but at small scales they are saturated!  The maria are more recent than the highlands (but still very ancient), and they were hit with fewer large objects.

A nearly full Moon photographed from the Apollo 11 Command Module shortly after TransEarth Injection:

 

A close-up view of the Apollo 11 landing site in the Sea of Tranquility, with the CSM in the foreground.  The mare floor looks smooth and unsaturated (low density of craters) from this distance.

Cross-sections of craters (from Wikipedia):

breccia -- a rock composed of originally-separate rock fragments that have been welded together (on the Moon, by high temperatures and pressures generated by impact events).  Rare on Earth but common on the Moon.

Some pictures of cratered regions on the Moon:

This picture shows both the lunar frontside (on left) and farside (on right).  Note saturated craters on farside.  The front side is dominated by the lower-elevation maria, which look smooth from a distance, but are actually saturation-cratered too (on much smaller scales).

Two largeish (~ 100-km diameter) Moon craters.  Note ejecta blanket, slumping of crater walls, and central peaks.

Lunar farside crater, 80 km in diameter:

 

A crater of similar size with a more ovious ejecta blanket:

 

Panoramic view from Apollo15  LM (Mt. Hadley to the left).  Note regolith and craters on small scales.

 

A World War I battleground with saturated craters created by explosions of French artillery shells.  Note German soldiers for scale.

View of Apollo 15 landing site.  Hadley rille is to lower left and Mt. Hadley is off the bottom.

Here are some geologic terms that we use to discuss the surface of the Moon and other primitive solar system bodies:

regolith -- literally, "blanket of stone".  A layer of gravelly, pulverized rock, many meters thick, produced by eons of impacts.

gardening -- a deceptively tranquil term for the violent impacts that produce regolith and the associated overturn and welding of rock fragments (breccia).

Remember the stages of planetary heating:

The Moon went through the first stage, but not the second stage.  So the heavily-cratered surface that we see still shows the effects of the accumulation phase of the Moon.  Evidence of this stage on the surface of the Earth has been erased by gigayears of resurfacing.

The Moon is highly depleted in volatile elements and is enriched in refractory elements.  This is a major piece of evidence for a high-temperature origin as already discussed.

The Moon is very dry -- no water is found in any of the lunar samples.  There is ambiguous evidence from the Lunar Prospector mission that some water molecules may survive in the bottoms of lunar craters near the Moon's poles where sunlight never penetrates.
 
 

Let's estimate how long it would take the Earth to erase its cratering record.  The Earth's lithospheric plates move at velocities of roughly 1 cm/year.  How long would it take for a plate to move one Earth radius, 6378 km = 6.378 X 10⁸ cm?  Answer: about 600 million years.  So the Earth has resurfaced itself many times over its total age of 4570 million years.  Craters that are as old as the Moon's surface, more than 3000 million years old, have been totally erased!

Origin of the 1:1 spin-orbit resonance

The tidal force is caused by the fact that gravitational attraction between two bodies is not constant, but varies as GmM/r², which means that the force is larger where r is small and smaller where r is large.  So the balance between orbital forces and gravitational attraction is exact only at the center of a planet.  There is a slight imbalance, resulting in an outward force on opposite sides of the planet -- the side toward the attracting body and the side away from it.  The Earth's rotation is slowing because of tidal forces from the Moon.  As a result, the Moon is slowly spiraling away from the Earth.

We can draw a similar figure for the tidal distortion of the Moon by the Earth:

Most probably, the Moon originally rotated like the Earth, once every few hours.  Such prograde rotation would have carried the Moon's tidal distortion away from the sub-Earth point, and the Earth's tidal pull would have slowed the Moon down until it rotated at the same rate as it orbits the Earth.  This must have happened billions of years ago.

The natural result of this process is that the Moon ends up with its heaviest ends pointed toward and away from the Earth.  The Moon's frontside is heavy because there are extra concentrations of mass under the maria.  These are called mascons.  The farside is heavier too, because the crust is thicker there: