The first, the natural monopoly, is like when for geographical reasons you only have one supplier, because the area doesn't need to support more. For example, one sports supply store in a small town. i.e. only one sports supply store can be supported by the area market.
The second, the artificial monopoly, is like when a large company decides to try and control the market, raising prices in an area where a natural monopoly doesn't exist. Sometimes they do it by forming an agreement with other similar suppliers, which is called a cartel.
The third, the state monopoly, occurs when competition is prevented one way or another by government (i.e. people with notions of 'government authority').
The first two can form in a laissez faire free market, but the inherent checks and balances which make the free market so beautiful cannot abide them for long and their attempts to control prices is very short lived. The third monopoly is inflicted upon the market with the deceitful claim that it is meant to keep the first two from happening, but in fact, creates longer lasting and more stable monopolies which are worse than the first two types combined.