That is not dead which can eternal lie
And with strange æons even death may die -- "The Call of Cthulhu" (1928), H.P. Lovecraft
Precambrian: general term for all time before the Phanerozoic Eon. Other names for Precambrian: Azoic (lifeless) or Cryptozoic (hidden life).
Special terminology for Precambrian rock exposures and distributions:
Precambrian Shield: Exposed surface of Precambrian bedrock
Platform: Shield covered by post-Precambrian rocks
Craton: Precambrian Shield + Platform
Orogen: Material accreted onto margins of craton by later orogenic episodes
Standard international stratigraphic nomenclature does not recognize a formal "Precambrian". Instead, uses three divisions: the Hadean (of Hades), Archean (ancient), and Proterozoic (earliest life) Eons.
Before The Hadean Eon: >4.56 Ga Formation of Proto-Earth (& the Rest of the Solar System):
Solar system coalesces out of remains of dust clouds produced by earlier generations of supernovae. Particles clump together to form planetessimals,
which are comprised of various combinations of:
Ices (frozen gasses, including water)
Organics (carbon-rich compounds)
As these lump together, they become more massive and exert more gravitational pull, attracting more material, becoming more massive, exerting more gravitational pull, etc. Soon the vast majority of this material is clumped into the various large bodies of the Solar System, with a tiny fraction left over to form today's asteroids, comets, and Kuiper Belt Objects. The Proto-Earth (called "Tellus" by some) is one of the largest bodies in the interior part of the Solar System.
A Star Is Born: However, the VAST majority of the Solar System's mass is in the Sun. Gravitational forces of this mass starts fusing hydrogen into helium, and the Sun ignites. Originally it was dimmer than today, but still it shone. Solar wind and photon pressure began to sweep the Solar System clear of much debris.
That time period before the oldest known rocks on Earth
A "zen" time period, in that it is defined by absence, and one which will always shrink as new discoveries of ever-more-ancient rocks are made.
Based on estimates of the age of the Earth, the Hadean begins 4.56 Ga. It ends 4.03 Ga (in terms of whole rocks) or 4.40 Ga (in terms of oldest individual zircon crystals) as of February 2001. Some charts show a round 4.00 Ga but this isn't justified by our current data, and no formal proposal has been ratified to make 4.00 Ga the base of the Proterozoic.
Not (quite) yet a formal unit under the International Commission on Stratigraphy, although this is expected to change soon
By definition cannot be represented by rocks!
The Iron Catastrophe: Although the Earth is not a star, it (or at least the Proto-Earth) too went through a profound change in its
earliest history. Originally the ices, organics, silicates, and metals would have been randomly mixed together, but a combination of gravitational heating, heating from impacts of planetessimals, and radioactive heating from some of the isotopes found in the silicates and metals caused the material of Proto-Earth to melt. The heaviest materials (mostly metals, especially iron and nickel) sank to the interior to form the core; the silicates "floated" on top to form the mantle. Ices melted into gasses and liquids, and they and organics got mixed in with other material. With a metallic core, Earth now had a magnetosphere.
The Primordial Atmosphere: Proto-Earth's original atmosphere would have mostly been hydrogen and helium, like the gas giants. However, it lost much of this atmosphere to a number of factors:
Its lower gravitational field than the gas giants
Solar wind would have stripped much of the atmosphere, at least until the magnetic field became strong enough
Energy from planetssimal impacts would send some of that gas into space
(And one impact that did much more than ALL the others...)
Bad Moon Rising: About 4.510 Ga, a Mars-sized planet (called "Theia" by some) collided into the Proto-Earth ("Tellus"). Theia and a substantial fraction of the Earth's mantle was vaporized. The matter that remained in orbit around the Earth coalesced to form the Moon; the rest rained back down to the surface of the Earth. (So the matter of Proto-Earth + Theia became redistributed to form today's Earth + Moon). (It is worth noting that recent studies suggest that instead of a single "Big Thwack", multiple large planetary bodies may have smashed into Tellus in a geologically short period of time.)
As a result of the birth of the moon:
Earth's mantle was turned molten to a great depth: a magma ocean. Partial melting of this ocean began to separate out certain lighter minerals, and Earth's crust (originally all oceanic) began to form.
Although Earth's primordial atmosphere was lost, degassing from the magma ocean (and additional material from comets) produced Earth's water oceans (once the magma ocean had cooled down!) and the second (reducing) atmosphere.
The water oceans would originally have been much deeper than today's, as there was no (or very little) continental-scale rock to sit above sea level, and before the rise of subduction not much way of pulling water out of the oceans and mixing it into mantle silicates.
The reducing atmosphere would have resembled that of Saturn's moon Titan: mostly methane, carbon dioxide, nitrogen, ammonia, water vapor.
Here's a video with an overview of the rest of the course, entitled "A Brief History of Geologic Time":