What do these numbers mean on a note?

[Fabi_an]

So I have this euro bill (series I) and the first letter is P on the serial number? Is the serial number the 12-digit one?
If so, what does the "P" mean? Is it from which country it is? If so, can I have the list over all of the countries?

[trezay]

Yes, the 12-character number is the serial number. For notes in the first series, the letter at he beginning of the serial number is the country that issued the note (the full list of letters is here). In your case, the P at the beginning of the serial number means it’s a Dutch note. For Europa notes, it’s the place where the note was printed. The full list for Europa notes is here.

[lmviterbo]

Just a small correction: the serial number, despite its name (serial number), is in fact the whole code, including the initial letter(s). This is in fact valid for other serial numbers in other currency, or in other products. As the article on Serial number on Wikipedia puts it,

Despite being called serial "numbers", they do not need to be strictly numerical and may contain letters and other typographical symbols, or may consist entirely of a character string.

Also, note that the serial number goes generally up as a batch of banknotes is printed, but there are complex numbering schemes that aren't just going up from 000… to 999…

Finally: the last digit of every Euro banknote is a check digit. Although it's part of the serial number, it doesn't belong to the numbering scheme (for example, EA000…001 is not followed by EA000…002; instead, it goes from EA000…001 to EA000…019 (the last digits, shown here in pale magenta, are check digits). So if you happen to withdraw a series of fresh new banknotes, you will notice this kind of numbering where the second-to-last digit is the one rising up, not the last one.