Demand:

Demand refers to the willingness and ability to buy a good or a service at a given price. Holding other factors constant, increase in price will decrease the quantity demanded and vice versa.

Market:

Market refers to all arrangements between buyers and sellers, in order to exchange goods and services, at a given price. Market leads to price formation.

Price index:

Price index is a weighted average of a collection of goods and services, in a given location and for a specified period of time. Examples of price indices are: consumer price index, producer price index, exports and imports indices.