Care to narrow your question down?

this is a insanely broad question, with a ton of different possible answers, but if you just want a interesting set of events to start looking at, I would start with (just off the top of my head... I am probably missing a ton). Roughly chronological. My favorite book on part of this era is: Freedom Just Around the Corner: A New American History, 1585-1828

1. The failure of the articles of confederation: (http://history.state.gov/milestones/1776-1783/articles)
2. The Consitutional Convention.
3. The Presidency of Washington
4. The Jefferson / Adams election (http://www.cnn.com/2008/LIVING/wayoflife/08/22/mf.campaign.slurs.slogans/)
5. The Louisiana Purchase.
6. The War of 1812.
7. The Era of Good Feelings 7a) Eli Whitney, and Industrial Revolution and the Cotton Gin
8. The Missouri Compromise.
9. The Erie Canal
10. The election of Andrew Jackson & the dissolving of the second bank of the United States. Trail of Tears
11. The Mexican-American war
12. Uncle Tom's Cabin. Dred Scott Decision, Lincoln's Election