Fiat Money
Explain to me how an increase in paper pieces can possibly make a society richer. If that is the case, why is there still poverty in the world? — Hans-Hermann Hoppe.
Fiat money is the currency that is exclusively issued and controlled by political authorities. It is also called Political Money or State Money.
Most governments establish decrees to privilege the adoption of its own currency. For example, legal tender laws impose the acceptance of a certain currency when it is offered (tendered) as payment to extinguish any debt. Legal tender status also implies that the Fiat Money is the Unit of Account used by official entities to calculate and impose taxes; therefore, exchange rate fluctuations may imply costs such as tax liabilities that create friction to the social adoption of other moneys.
Additionally, direct restrictions to the use of competing currencies are frequently imposed.
The fiat system is controlled through a Central Bank by a state or a group of states.

The Central Bank has the monopoly over monetary inflation, i.e. over the issuing of fiat monetary units. Fiat units can be either physical in the form of notes and coins, or digital in the form of commercial banks reserves at the Central Bank. The sum of both forms is called base money.
In pure physical monetary systems, like gold, monetary inflation is limited due to the difficulty of extracting new units from singular locations. But in a fiat system there is no limit beyond the central bank's self-imposed verbal commitment to not abuse the printing-press by going BRRR.
Although paper fiat units may be printed to ensure their exchangeability with digital reserves, nowadays the "printing" tends to be done electronically by simply modifying Central Bank's database.
Central Banks' plan for assigning the new created fiat units is known as monetary policy.
Central banks' have the self-imposed mandates of ensuring monetary and financial stability, although the Federal Reserve has the additional mandate of achieving maximum employment. However, in practice, they prioritize the monetization of their own state's large deficits whenever they occur.
Central Banks define monetary stability as a constant inflation of "consumer prices" and as a non-volatile exchange rate in the short-term against other fiduciary currencies.
Financial stability is understood as the smooth operation of financial entities that are considered too big or too connected to let them fail.
The implicit promise of bailout to those entities in the event of bankruptcy encourages them to incur in greater risks and to conceal capital consumption under the guise of accounting profits.
Central Banks' plan to temporarily decrease unemployment through monetary policy is to increase the abundance of fiat monetary units in order to rot its value. That devaluation implies an accounting trick in which fiat obligations are partially forgiven, benefiting the future payers of already stablished contracts at the expense of their counterpart; e.g. benefiting borrowers at the expense of lenders, or employers at the expense of their respective already hired employees.
Fiat is a dysfunctional monetary system:
A monetary system is simply a set of balances that can be transacted voluntarily by their owners. A balance, in turn, is simply a given number of monetary units.
Physical fiat balances can be possessed by their owners, but their paper form provides them poor storability and enables only local transferability.
So the only alternative for significant amounts is the indirect use of fiat digital balances through checking accounts, since individuals do not have access to comercial banks reserves. Those reserves can only be possessed and transacted by the Central Bank, that settles the net result of transfer requests made by commercial banks.
Checking accounts or demand deposits are claims on a definite amount of money, supposedly redeemable on demand, so they are generated through lending.
If the claim issuers (banks and financial institutions) keep the full amount of borrowings as reserve, then those accounts are called money-certificates, however the fiat borrowers usually keep only a small fraction of the borrowings as reserve and invest the rest, which imply the existence of various liquid claims per each fiat unit.
Therefore almost all of what is generally perceived as available monetary value is in the form of claims which total sum is called bank "money".
The money multiplier concept suggests that bank "money" is equal to the base money divided by the average reserve ratio, where reserve ratio is equal to bank borrowings divided by their reserves. Nevertheless, base money and bank money do not maintain a constant relation.
The recognition that "consumer prices" are more sensitive to changes in the total amount of bank money + cash than in the base money led to the study of money aggregates like M2, that is also known as money supply or broad money. Money aggregates consist in the accounting combination of different kind of accounts and financial assets with cash.
Nowadays Central Banks' main tool for influencing the amount of bank money in short-term, is the manipulation of the rate at which comercial banks lend reserves each other.
By lowering those interest rates, the market capitalisation of the existing debt tends to grow and the incentives for borrowing increase, so bank "money" is created.
The opposite effect happens by increasing interest rates.
Trusted third parties are security holes:
With the emergence of the digital age, the use of cash is being progressively legally restricted.
Regulations like KYC requirements force financial services to snitch out clients and to collect data that eventually becomes public, as nobody can ever guarantee its protection.
People gather your data on the promise that they will never share it, when in fact they cannot, and will not retain control of it for long. — Nick Szabo
Other legislations, like AML, imply capital controls that result in huge bureaucracy and censorship.
Centralized financial assets are ultimately controlled by a few actors that simply grant real owners the permission to access software that displays ledger entries of their property, so data centers have become highly centralized honeypots under the control of the state that use them as surveillance weapons that invade privacy and regulate behaviour.
Don't put most of your family's wealth in assets that some stranger can turn on and off like a switch. — Nick Szabo.
Nevertheless, every time a money becomes more of a medium of censorship, it becomes less of a medium of exchange. A superior form of money was needed.