What were the first local currency systems in history we have detailed information on? I don't think it was gold/silver or other hard to produce materials. Probably these became more important currencies after intercontinental and intercultural trade was more common.
The first evidence of usage of currency dates back to the code of Lipit-Ishtar, a set of laws dating to about 2000 BC. In this code there is mention of shekels of silver paid in compensation for various infractions. Since this is stated so clearly in a law created by a king, it must be presumed that such currency was in common use already by the people of Mesopotamia. Now, while there is much dispute over the creation of the first coin, it has to be admitted that a system of currency does not necessarily require coins, but some intermediate thing that can be exchanged for goods, and thus shekels of silver would qualify.
In fact, according to The Future of Money by Bernard Lietaer, the first coin is a 3000 BC sumerian coin with the image of a bushel of wheat on one side, and the word Shekel can be broken down to 'She', meaning wheat, and 'Kel', meaning bushel. Thus we already see that silver could be substituted for such a unit and it is probable that before 3000 BC a bushel of wheat or some other key produce was the actual unit of exchange.
We still have to guard against thinking that Mesopotamia was the first place for the use of currency, as it is conceivable that in other parts of the world (for example the Indian subcontinent or the Chinese plateau) currency had been invented independently. What we know for sure is that use of currency and even coinage was far older than Lydian currencies, since Lydian coins were produced in large quantities for a society well used to currency as a means for trade. Lydian coinage, however, was the ancestor of Greek and Persian coinage, which in turn were the ancestors of all European and Islamic coinage.
The first evidence we have for the usage of actual coinage as currency is the "Lydian Lion", a stamped coin of electrum from, as the name would imply, the region of Lydia in Anatolia. Herodotus indicates these started showing up in the early 7th Century BCE.
See here for more info on the history of the first Lydian coinage: http://www.e-allmoney.com/coins1.html
I'm sure that prior to the Lydians actually stamping coins to validate their weight and purity, and thus their intrinsic value people had probably been using precious metals in bullion form to pay for things, but this wouldn't quite be the same as having a handy, pre-validated chunk of electrum that had a known value without having to weigh it and such.
I'm unsure of the details, but the Greek city states started minting their own coinage not too long afterwards. One of the most prolific being Athens' "Owl" which served as a standard international currency in the eastern mediterranean for centuries.
As far as I'm aware, all of these were useful as a medium of exchange because of the intrinsic value of the metal they were made from.
Sometime during Rome's early or middle republican era (first Samnite war perhaps?) is one of the earliest, if not the earliest time we see a state issuing a currency that has value because they say it's worth X amount, rather than being strictly based on the weight and purity of the metal.
I could be off on that last bit, I'm at work now and don't have the time to go digging up the references, but I recall an incident during one of the Roman Republic's many wars that led to citizens hoarding their coinage, which led to a severe shortage of the source of the valuable metals they were made from that Rome needed to pay for its war. So they came up with a clever plan of debasing their currency and declaring that a Sestercii were worth not 10, but 16 asses, and they had this great deal for anyone who wanted to come and trade in all their old coins, 16 for the price of 10! They soon had the funds they needed :).
Currency comes in many different forms, and since you mention "abstract" currency here, that excludes coins that were traded for their metal value, which is the case of most early coinage, where the stamp was a mark guaranteeing that it was reasonably pure metal.
The first abstract coinage is probably dependent on your opinion on what "abstract" means. The Roman empire quite quickly started debasing it's coinage so that the face value was higher than the metal value, and that could be argued as making it "abstract". On the other hand this practice sometimes led to inflation, so it's clear that the metal value wasn't irrelevant.
Other cases of abstract money are when you start using paper as emergency currency, basically printing paper notes as future promises of real money. Thusly they were still tied to metal value, even though it is abstract in the meaning that the value was not in the paper.
When the usage of banknotes was (re)invented in Sweden in 1660, they were also a form of promissory notes and you could (in theory) redeem them in real coinage. However, the Stockholm Banco bank folded in 1664 and was taken over by the state, which continued the practice of printing paper money without being actually able to cover for it, should everybody ask for coins at the same time. This could also be seen as the first "abstract" money as there was no real coverage for it. However, the bank notes continued to be nominally tied to metal value, even though this was often not actually true during times of crisis. Many countries suspended the exchangeability of notes to gold or silver during WWI, for example.
Properly abstract currency, i.e. currency that does not have any notional intrinsic value at all and does not pretend to have it, didn't arrive until 1971, when Nixon ended the convertibility of dollars to gold. Since most currencies in the world at that time had a fixed exchange ration to dollars, that also in practice meant that almost all currencies in the world became truly abstract in one go.