Describe the factors that shaped Europeans' individual and collective identities and those of the peoples they encountered in their overseas expansion.
Hi :) I hope I have understood your question correctly, your phrasing is a bit ambiguous.
First of all- European identity. It has been traditionally argued that European identity has been shaped by Christianity, Roman law and Greek philosophy. (Humanism and Enlightenment are also an important part of European identity, but we won't be looking at them since your question concerns Europe in the 1600's). The European Renaissance (14th to the 17th century) came after a Medieval era very strongly dominated by Christianity (practically, it was the Christian Church who had more political power than anyone else) and started to re-discovered the Ancient Greek and Latin philosophy/literature/way of thinking. The Ancient Greek and Roman models became standards of how philosophy, political thinking and art -literature, theatre, painting, sculpture etc. should be done; while the Church did maintain a great deal of political power.
At the same time, the great geographical discoveries happened: so Europeans found themselves faced with people who werenotChristian, werenotspeaking European languages and werenotleading their lives by the same principles and customs as the European. (That's not to say that they were any less developed or functional as a society: for instance,the Mayans had built cities and massive pyramids and had a complex economy). Nonetheless, to the European mind at the time, they were perceived assavages, defined asnon-Christian, non-European.
The Portuguese and Spanish conquistadors considered the natives of conquered territories to be sub-human, therefore concluding that killing or enslaving them must be morally justified; on the basic argument that because they were not endowed with reason (you can relate this to how the European concept of reason has been shaped by Greek Philosophy, to which the native could not have had contact with before) and because they were 'damned' for not worshipping the Christian god. (As you can imagine, the fact that conquistadors were after the gold, spices and other riches in the conquered areas or wanted to get into the slade trade played a big part in thir position as well). Their ideas have been opposed by some, such as bishop Bartolome de las Cassas, who argued that natives could and should be treated as full human beings, but only due to their potential to convert to Christianity and adopt the European ways.
The genocide committed by Europeans in the colonised territories and the centuries of domination that followed meant that people in the colonised area had very little freedom to define themselves otherwise than by oposition to Europeans. Frantz Fanon, an Algerian psychoanalist and psychiatrist who wrote in the 60's argued that the imposition of a subjugating colonial identity is a societal effect of colonisation, and that it is harmul to the mental health of people who have lived under a colonial regimes, even generations after the area is no longer a colony or under obvious Western domination.