More specifically, these were used by the Romans. On the fifth day of a male's infancy, a praenomen was given to said child from a list of 18. Each name had an abbreviation that occasionally utilized Greek letters (such as kappa and gamma). Since I happen to have a list handy (as all unjustifiably avid Latin students do) here they are, with their abbreviations preceding the praenomen:
A.  Aulus      Mam. Mamercus
Ap. Appius     N.   Numerius
C.  Gaius      P.   Publius
Gn. Gnaeus     Q.   Quintus
D.  Decimus    Ser. Servius
K.  Caeso      Sex. Sextus
L.  Lucius     Sp.  Spurius
M.  Marcus     T.   Titus
M'. Manius     Ti.  Tiberius
the 'C' and 'K' abbreviations come from the aforementioned gamma and kappa, respectively.

If two children in a family had the same praenomen, one would be given a cognomen, the name they would go by. This would precede the nomen gentile, or family name, and would also distinguish different branches of one family. Many cognomena could be held by a single person, such as Publius Cornelius Scipio Africanus Aemilianus. He was adopted from the Aemilius family into the Scipio branch of the Cornelius family. The Africanus cognomen comes from the reputation Scipio made for himself in the Punic Wars with Carthage, which, you guessed it, was in Africa.

One significant thing to point out is that all of these rules and names applied only to males. Females took the feminine form of their nomen gentile, thus all of the daughters of Scipio would be named Cornelia. They would be told apart in a degrading way; they would be numbered (ordinally). Thus, the first Cornelia was Cornelia Prima, the second Cornelia Secunda, et cetera ad infinitum (cum multis nauseis).

Freed slaves (yes, the Romans were a bit more wholesome than more modern slave owners) adopted the praenomen and nomen gentile of their former master, keeping their own names as cognomena. Therefore, if the aforementioned Scipio freed a slave named Foo (I'm sure Foo was a popular name back then), then the slave's name would be Publius Cornelius Foo.

Well, that was fun. Now all I need is another book/article that I can summarize into a node.