Under the earth crust is the mantle.There is what layer??

Under the crust is the Upper and Lower Mantle which covers the Earth's Core, which is about 1220 km in radius.

The lithosphere contains the crust: http://en.wikipedia.org/wiki/Lithosphere

According to Wikipedia: http://en.wikipedia.org/wiki/Earth%27s_core
"The existence of an inner core that is different from the liquid outer core was discovered in 1936 by seismologist Inge Lehmann using observations of earthquake-generated seismic waves that partly reflect from its boundary and can be detected by sensitive seismographs on the Earth's surface. The outer core was thought to be liquid due to its inability to transmit elastic shear waves because only compressional waves are observed to pass through it. The solidity of the inner core has been difficult to establish, because the elastic shear waves that are expected to pass through it are very weak and difficult to detect. Dziewonski and Gilbert established the consistency of this hypothesis using normal modes of vibration of Earth caused by large earthquakes. Recent claims of detections of inner core transmitted shear waves were initially controversial but are now gaining acceptance."

According to Wikipedia: http://en.wikipedia.org/wiki/Structure_of_the_Earth
"0–60 km 0–37 miles: Lithosphere (locally varies between 5 and 200 km)
0–35 km 0–22 miles: ... Crust (locally varies between 5 and 70 km)
35–60 km 22–37 miles: ... Uppermost part of mantle
35–2890 km 22–1790 miles: Mantle
35–660 km 22-410 miles: Upper Mantle
100–200 km 62–125 miles ... Asthenosphere
660–2890 km –1790 mile: Lower Mantle(Mesosphere)
2890–5150 km 1790–3160 miles: Outer core
5150–6360 km 3160–3954 miles: Inner core "

the crust and upper mantle make up the lithosphere, and then comes the asthenosphere and then the lower mantle, next is the core of course.

The Earth is composed of four different layers. Many geologists believe that as the Earth cooled the heavier, denser materials sank to the center and the lighter materials rose to the top. Because of this, the crust is made of the lightest materials (rock- basalts and granites) and the core consists of heavy metals (nickel and iron).

The crust is the layer that you live on, and it is the most widely studied and understood. The mantle is much hotter and has the ability to flow. The Outer and Inner Cores are hotter still with pressures so great that you would be squeezed into a ball smaller than a marble if you were able to go to the center of the Earth!!!!!!