During the period of European colonialism, several European powers invaded and established settlements in the Americas. Below is a list of the major colonial powers, their arrival dates, the duration of their presence, the areas they settled, and the manner in which they acquired territory:
1. Spain
- Year of Arrival: 1492 (Christopher Columbus)
- Duration: Over 300 years (until the early 19th century, when most Spanish colonies gained independence).
- Areas Settled:
- Caribbean: Hispaniola (present-day Dominican Republic and Haiti), Cuba, Puerto Rico.
- Central America: Mexico, Guatemala, Honduras, Nicaragua, Costa Rica, Panama.
- South America: Colombia, Venezuela, Peru, Ecuador, Bolivia, Chile, Argentina, Paraguay, Uruguay.
- North America: Florida, California, Texas, New Mexico, Arizona (present-day U.S. Southwest).
- Manner of Acquisition:
- Conquest of indigenous empires (e.g., Aztec and Inca).
- Establishment of colonies through exploration, military force, and alliances with local groups.
- Encomienda system (forced labor of indigenous peoples).

2. Portugal
- Year of Arrival: 1500 (Pedro Álvares Cabral in Brazil).
- Duration: Over 300 years (until Brazil’s independence in 1822).
- Areas Settled:
- Brazil (coastal regions initially, later expanding inland).
- Manner of Acquisition:
- Treaty of Tordesillas (1494) divided newly discovered lands between Spain and Portugal.
- Colonization through the establishment of sugar plantations and exploitation of indigenous labor, later supplemented by African slaves.

3. England (later Great Britain)
- Year of Arrival: 1607 (Jamestown, Virginia).
- Duration: Over 150 years (until the American Revolution in 1776).
- Areas Settled:
- Eastern North America: Thirteen Colonies (present-day U.S. East Coast).
- Caribbean: Jamaica, Barbados, Bahamas, and other islands.
- Manner of Acquisition:
- Settlement through colonization companies (e.g., Virginia Company).
- Displacement of indigenous peoples through warfare, treaties, and disease.
- Expansion through agricultural development and trade.

4. France
- Year of Arrival: 1534 (Jacques Cartier in Canada).
- Duration: Over 200 years (until the loss of most territories in the mid-18th century).
- Areas Settled:
- North America: Quebec, Acadia (present-day Maritime Canada), Louisiana Territory (Mississippi River Valley).
- Caribbean: Haiti (Saint-Domingue), Guadeloupe, Martinique.
- Manner of Acquisition:
- Fur trade alliances with indigenous peoples.
- Settlement and military outposts.
- Cession of territories to Britain and Spain after conflicts (e.g., Seven Years’ War).

5. Netherlands (Dutch)
- Year of Arrival: 1609 (Henry Hudson in present-day New York).
- Duration: About 50 years (until the English seized New Netherland in 1664).
- Areas Settled:
- North America: New Netherland (present-day New York, New Jersey, Delaware, Connecticut).
- Caribbean: Curaçao, Aruba, Sint Maarten.
- Manner of Acquisition:
- Establishment of trading posts and settlements.
- Purchased land from indigenous peoples (e.g., Manhattan).

6. Russia
- Year of Arrival: 1741 (Vitus Bering in Alaska).
- Duration: About 125 years (until the sale of Alaska to the U.S. in 1867).
- Areas Settled:
- Alaska and parts of the Pacific Northwest (briefly).
- Manner of Acquisition:
- Fur trade and small settlements.
- Limited colonization compared to other European powers.

7. Sweden
- Year of Arrival: 1638 (New Sweden colony).
- Duration: About 17 years (until absorbed by the Dutch in 1655).
- Areas Settled:
- Delaware Valley (present-day Delaware, New Jersey, Pennsylvania).
- Manner of Acquisition:
- Small-scale settlement and trade with indigenous peoples.

8. Denmark
- Year of Arrival: 1672 (Danish West Indies).
- Duration: Over 200 years (until the sale of the Virgin Islands to the U.S. in 1917).
- Areas Settled:
- Caribbean: Saint Thomas, Saint John, Saint Croix (U.S. Virgin Islands).
- Manner of Acquisition:
- Establishment of sugar plantations using enslaved African labor.

Summary of Territorial Acquisition:
- Conquest: Spain and Portugal used military force to conquer indigenous empires.
- Settlement: England, France, and the Netherlands established colonies through settlement and trade.
- Treaties and Purchases: Some territories were acquired through treaties (e.g., Treaty of Tordesillas) or purchases (e.g., Manhattan, Alaska).
- Displacement: Indigenous peoples were often displaced through warfare, disease, and forced labor.
This list covers the major European colonial powers and their activities in the Americas during the colonial period.