A business with many share holders. Corporations are formed to raise capital for expansion. Share holders receive dividends when the company makes a profit, and can only lose what they put in.
A monopoly is when a company or corporation controls an entire market. This allows them to raise prices to any level. Government regulation prevents all but a few monopolies such as utility companies.
Companies in a single market making an agreement on prices and the division of business. Railroad companies practiced this until it was outlawed by the government.
Corporations in the same market or related markets would form a trust that put control of business under a single group of trustees. Share holders still received dividends, but had no say in the business. Trusts were later outlawed.
A holding company would buy enough stock in different companies to control them. This was done to get around the outlawing of trusts. Eventually, holding companies were outlawed also.
A corporation that owns many different unrelated businesses. Conglomerates are formed by mergers, where one company would take over another. These are still in practice today.