A pure monopoly means a single seller with no competitors. Monopoly power may exist when firms have 25% or more market share - this definition is useful for the purposes of regulating of mergers. A complex monopoly is a situation where a number of firms act as though they were a single firm - for example, by jointly raising prices at the same time. A legal monopoly is a firm that is granted monopoly status by a government. A natural monopoly is a firm which owns a single infrastructure, such as a gas or electricity provider.
Read more on Monopolies