Carbon was not created in the big bang due to the fact that it needs a triple collision of alpha particles (Helium nuclei) to be produced. The universe initially expanded and cooled too fast for that to be possible. It is produced, however, in the interior of stars in the horizontal branch, where stars transform a helium core into carbon by means of the triple alpha chain.
Carbon has four electrons in its outer shell, and except in a few reaction intermediates, is tetravalent. It has great affinity for bonding with other small atoms, including other carbon atoms, and thanks to its small size is capable of forming multiple bonds. Thanks to these there is an unrivaled diversity of carbon compounds, studied in Organic Chemistry.
The most prominent oxide of carbon is carbon dioxide, CO2. This is a minor component of the Earth's atmosphere, produced and used by living things, and a common volatile elsewhere. In water it forms trace amounts of carbonic acid, H2CO3, but as most compounds with multiple single-bonded oxygens on a single carbon it is unstable. Through this intermediate, though, resonance-stabilized carbonate ions are produced. Some important minerals are carbonates, notably calcite. Carbon disulfide, CS2, is similar.
The other oxides are carbon monoxide, CO, and the uncommon carbon suboxide, C3O2. Carbon monoxide is formed by incomplete combustion, and is a colorless, odorless gas. The molecules each contain a triple bond and are fairly polar, resulting in a nasty habit of binding permanently to hemoglobin, so that the gas is poisonous. Cyanide, CN-, has a similar structure and behaves a lot like a halide ion; the nitride cyanogen, (CN)2, is related.
There is an unbelievable diversity of hydrocarbons, starting with methane, CH4. In these the carbon atoms are bonded into long chains, branches, or rings, often with double and/or triple bonds. Of particular note are the aromatic hydrocarbons, in which the carbon atoms form rings stabilized by pi bonding. In the limit these blend into the various forms of pure carbon. There are even more hydrocarbon derivatives, including things like halides, alcohols, and acids.
With strong metals carbon forms either carbides, C-, or acetylides, C22-; these are associated with methane and acetylene, both incredibly pathetic acids. All in all, with an electronegativity of 2.5, carbon prefers to form covalent bonds. A few carbides are covalent lattices, like carborundum, SiC, which resembles diamond.
At normal pressures carbon takes the form of graphite, in which each atom is bonded to three others in a plane composed of fused hexagonal rings, just like those in aromatic hydrocarbons. Thanks to the delocalization of the pi-cloud graphite conducts electricity. The material is soft and the sheets, frequently separated by other atoms, are held together only by van der waals forces, so easily slip past one another.
At very high pressures carbon has a second allotrope called diamond, in which each atom is bonded to four others. Diamond has the same cubic structure as silicon and germanium and, thanks to the strength of the carbon-carbon bonds, is together with the isoelectronic BN or boron nitride the hardest substance in terms of resistance ot scratching. The transition to graphite at room temperature is so slow as to be unnoticeable. Under some conditions, carbon crystalizes as Lonsdaleite, a form similar to diamond but hexagonal.
Carbon sublimes at 4100 K. In gaseous form it usually consists of short atomic strings called carbynes. Unless cooled very slowly these coalesce to form irregular, warped graphitic sheets that compose soot. Of particular note among these are forms where the sheets are bent into a stable self-enclosed form (eg a sphere or tube), called fullerenes. These are also known as "buckyballs" or "buckytubes", and have properties that have not yet been fully analyzed.