M0 is the narrowest definition of money supply in common use.
The definition used in the UK is bank notes and coins in circulation, plus banks' deposits with the Bank of England.
M0 is also known as the monetary base. This term refers to the fact that the money measured by M0 supplies the base on which other forms of money (such as bank deposits) are based.
The government is able to control the size of monetary base, and this makes controlling it a key policy issue and an important part of monetary policy.
Governments can increase the monetary base by issuing notes and coins and by issuing money in the form of banks' deposits with the central bank.
A key way in which the monetary base is expanded is by central bank purchases of government bonds (called gilts in the UK) in its open market operations. The central bank buys securities. It pays with increase in banks' deposits with the central bank, which it can do by fiat (i.e. simply by changing the numbers).
This process can be reversed by selling government bonds. The private sector pays the government to buy them, and this money can be taken out of circulation.
Central banks may also enter into repos or reverse repos when the need to influence the money supply is temporary.
In order to prevent excessive growth of the money supply, and therefore high inflation, governments usually have inflation targets. The issue and purchase of government securities is carried out in order to control interest rates, which in turn influences inflation.
This implies that growth in money supply is restricted to a level consistent with the desired rate of inflation.
Governments that are short of revenues sometimes simply have the central bank act as a buyer of any government bonds that are not bought by other buyers — funding spending from seigniorage profits. This is what is generally called printing money or quantitative easing. The problem with this is that the increase in the money supply causes inflation, usually very high inflation.