What major political party systems developed in this country between 1800 and 1860?

Political scientists generally say that there were three
party systems during this time.

The first party system
pitted the Federalists against the Democratic-Republicans.  This started during the
Washington administration as Alexander Hamilton and Thomas Jefferson started de facto
political parties that became more formal in the early 1800s.  This system lasted until
1812 or 1816, depending on how you define it.

The second
party system is known as the Era of Good Feelings.  After the Federalist Party died off,
the Democrats dominated American politics and there was no other serious party.  This
lasted until the 1824 election made Jacksonians angry at the supporters of John
Adams.

This split in the Democratic Party led to the third
party system.  This had the Democrats being opposed by the Whigs.  This system lasted
until the Civil War, although it was falling apart by the late '50s as the Whigs broke
up and were succeeded by the Free Soil Party and, eventually, by the
Republicans.