Final answer:
Antigua and Barbuda is the country encompassing the islands of Antigua as the largest, Barbuda as the second largest, and Redonda as the third.
Step-by-step explanation:
The country that has Antigua as its largest island, Barbuda as its second largest, and Redonda as its third is Antigua and Barbuda. These islands are located in the Eastern Caribbean Sea and are part of what is known as the Lesser Antilles. The Lesser Antilles is a group of smaller islands that contrast the larger islands of the Greater Antilles, which include Cuba, Jamaica, Hispaniola (containing Haiti and the Dominican Republic), and Puerto Rico. Antigua and Barbuda is an independent country, and tourism is one of the major industries for these islands, especially due to their beautiful beaches and favorable climate.