Describe and explain how the revolutionary era (1760–1801) shaped America. Consider the major changes that took place, particularly relating to American identity and the concepts of freedom and equality. How does that era continue to affect us today?

Ultimately, I would say that the United States itself was shaped by the experience of the American Revolution. If we go back further into the Colonial Era, the idea of independence would have been largely unimaginable, for colonists perceived themselves as Subjects to the British government, and the colonies themselves as extensions of Great Britain itself. This changed in the aftermath of the French and Indian War, when Britain started more strictly enforcing mercantilist laws and collecting taxes on the colonies, ending a long tradition of general nonintervention with the colonies. In those years, colonial discourse began to advance the argument that the colonists' own political rights (the traditional rights guaranteed to all Englishmen) were being transgressed. This souring of opinion on the British government ultimately resulted in the American Revolution.
Thus, if we look at this period in time, we are looking at a very real and profound transformation in terms of the American mentalities, away from a colonial mindset, which supported the growing push for independence. After winning the Revolutionary War, however, the newly independent Americans then needed to devise an effective means of governing themselves, and actually instituting a functioning democracy, one which would not dissolve into tyranny (this was one of the critical concerns of the Revolutionary period, and one of the critical questions facing American democracy). With the Constitution, the colonists found a solution to this question, taking the ideas of Montesquieu, creating a system of checks and balances to divide power among the various branches of government.
When we look at the core democratic values and principles which define our country, there's actually a lot of continuity. The Declaration of Independence, the Bill of Rights, and the Constitution continue to represent the cornerstones upon which much of our political principles and political traditions rest.

The revolutionary era greatly expanded the idea of freedom and equality, at least for white men. The American Revolution was in many ways an embodiment of Enlightenment ideals, including the idea of the social contract written about by Locke and others. The social contract involved the idea that the government relies on the consent of the governed.
Starting in the 1760s, many groups in the American colonies began to revolt against British economic restrictions that were tightened after the French and Indian War (also called the Seven Years' War). By protesting the Navigation Acts, the Americans showed that they were willing to revolt against Britain to exercise economic and political rights. The revolution was the outgrowth of people's belief in the social contract, and the Declaration of Independence included an enumeration of the different ways in which the British throne had violated the social contract and the inalienable rights (or rights that no one can take away) of the colonists.
The Constitution created the first (modified) democracy in the modern world (Athens had also been a kind of democracy). It specifically gave rights to people in the Bill of Rights that created greater freedom and equality for white men than had ever existed to date. The attitude of this age is still with us, and you can perhaps think of modern-day examples of how Americans are still trying to expand rights to different groups (including, for example, transgender and gay people today and women and African Americans in the past).