From Stephen Unger blog
As is the case for other religions, Quakers (members of the Religious Society of Friends) differ among themselves over various religious issues. For example, some, but not all, believe in some form of existence after death. There are Quaker congregations that have ministers presiding over their meetings, while others have no ministers. Such matters are not treated in this essay. Nor will I discuss differences associated with Friends located in such places as Kenya (where there are roughly twice as many Quakers as in the US).The Beginning
The Quaker religion was founded in England about 1650 by George Fox (1624-1691) . It arrived in America in 1656, with William Penn (1644-1718) , an associate of Fox, playing a major role in establishing it there.
English Quakers originally came to Boston, then dominated by Puritans, who treated them very badly. But they stubbornly kept coming, despite the imprisonment of many, and the execution of at least 4 of them. Eventually, partly due to help from the English King, Charles II, a Catholic supporter, Quakers were grudgingly accepted .
By 1675, the persecution of Boston Quakers led Penn to obtain from the King payment of a large debt to Penn's family, in the form of a large grant of land that formed much of Pennsylvania (including Philadelphia) and about half of New Jersey. Penn made this land available to settlers, including Quakers and other religious groups that were mistreated elsewhere .How Are Quakers Different?
Agreeing to disagree about what happens after death, Quakers concentrate on making this world better, rather than making assumptions about what happens to us after we leave it .
Friends might be characterized as action oriented. This is reflected in the way they behave at their meetings (religious services). Typically, instead of listening to a preacher, or praying, they silently meditate. Occasionally, a member of the congregation will be moved to stand and make a statement.
Rather than focussing on ritual, Quakers, as a group, devote their energy to various specific societal issues. Simplicity, truth, equality, and community are all important to Quakers. Centuries before others became concerned about such matters, they endeavored to live in a manner less harmful to the environment . In 1772, a prominent Quaker, John Woolman, wrote: "The produce of the earth is a gift from our gracious creator to the inhabitants, and to impoverish the earth now to support outward greatness appears to be an injury to the succeeding age." Equality of Women
A fundamental aspect of Quakerism is the belief in the equality of all people. They never believed that any subset of people was inferior, and they acted in accordance with this idea. 
From the origins of the Quaker movement in the middle of the seventeenth century, women were heavily involved, often in leadership positions. One consequence of this is that when, in the nineteenth century, there was a concerted women's liberation movement, Quaker women were in the forefront. A principal objective was to win the right to vote . This was achieved via passage of the 19th Amendment in 1922.Indians
Unlike almost all other Europeans who came to the new world, the Quakers, from the outset, treated the Indians fairly, showing respect for their religions and customs, and got along very well with them. There was mutually beneficial trading with the Indians. The Quakers learned their languages and taught the Indians a lot about farming techniques .Slavery
Almost from the birth of Quakerism, Quakers were outspoken opponents of slavery. And they didn't just talk about it. For example, between the late eighteenth century and the start of the Civil War, Friends were prominent in the organization and operation of the underground railroads by means of which tens of thousands of slaves, perhaps over a hundred thousand, were freed and assisted in getting to Canada .Nonviolence
Quakers have always avoided violence. They generally refuse to serve in the armed forces and refuse to pay taxes that they feel will be used to pay for a war. This sometimes leads to dilemmas. As ending slavery was a key factor motivating the North in the Civil War, many Quakers felt compelled to support the cause of the North, by paying taxes, or even by enlisting in the Northern army. Others supported the war effort by serving in the military as medics . Quakers seem to do well at handling situations in which people disagree as to what should be done.
Having had a lot of firsthand experience as prisoners under harsh conditions, Quakers were among the first to work actively on prison reform. William Penn and other Quakers ensured that prisoners in Pennsylvania were treated humanely. Efforts were made to educate them for constructive work after release. At a time when England imposed the death penalty for over 200 crimes, capital punishment was imposed in Pennsylvania only for murder or treason .Quakers Today
In 1700, when there were about 250,000 Europeans in North America, about 55,000 of them were Quakers. Currently, there are about 330,000,000 Americans, of whom about 75,000 are Quakers. So, during the past 3 centuries, while the population of the US grew by a factor of roughly 1,300, the Quaker population grew by a factor of only about 1.3. I could not find any Quaker population data for the intermediate years. Nor have I found any explanation of why the American Quaker population has increased so little over 350 years.