Just to set things straight, Europe did not colonize any area collectively. This is because Europe is a continent made of many nations, who were in competition to get the most colonies. Europe had two ages of Imperialism: the first focused on the Americas while the second focused on Africa and Asia.
1st Age of Imperialism:
The main European countries who colonized the Americas were Spain, France, Great Britain, Portugal, and the Netherlands. Other minor players included Russia, Denmark, Sweden, and Germany. The entire continents of North and South America were colonized, including all the Caribbean islands. Most countries on the American mainland became independent by the mid 1800s, but most island nations did not become independent until the mid 1900s.
2nd Age of Imperialism:
The main European countries who colonized Africa and Asia were Great Britain, France, Germany, and Russia Other minor players included Italy, Spain, Belgium, the Netherlands, and Portugal. Almost the entire continent of Africa was colonized and the majority of the Asian continent was either colonized or acted like satellite states. Most countries became independent in the mid 1900s.
Europeans have effectively colonized every area outside of Europe with only a few key exceptions, such as Ethiopia, Japan (and Korea and Taiwan because they were Japanese colonies), southern Patagonia, northern Canada, and empires like Persia, Qing China, and the Ottoman Empire because they were too big to swallow, but would have spheres of influence.
The first Europeans to colonize India were the Portuguese at Goa, followed by the Dutch, French, and finally, the British.
Two major reasons for Europeans to colonize the American continent are freedom and opportunity.
disease
Europeans were able to colonize Africa without fighting with one another.
The First European group to colonize Brazil was...The Spanish
Nothing "made Europeans colonize"; it was an active decision that they chose to do. They did this for material resources, labor resources, prestige, strategic positions, and religious evangelism.
Brazil
The adult sponges can colonize other areas by swimming to them.
They wanted to colonize it.
Spain - Hernan Cortez
to be jackasses
The Europeans respected that America had already colonized that territory and created a viable nation-state there.