What major political developments took place during Thomas Jefferson's administration?

Thomas Jefferson's victory in the United States' presidential election of 1800 marked the triumph of his anti-Federalist forces against the Federalist Party. Many of Jefferson's policies during this time were focused, therefore, on undoing the policies of his ideological adversaries and, during the Jefferson presidency, the Federalist Party began to decay and eventually went extinct.
Jefferson oversaw the unraveling of the fiscal policies of Alexander Hamilton. Specifically, he began a program of cutting spending and eliminating taxes, such as the excise tax on whiskey, with the ultimate goal of eliminating U.S. foreign debt. In foreign affairs, he instigated the political isolation of the United States, supporting the Embargo Act which effectively sealed American borders. Despite this, however, he still committed U.S. military forces to war against the Barbary states and negotiated the Louisiana Purchase from France, almost doubling the territory of the United States overnight.
Finally, although it sat outside the direct control of Jefferson, an important political development during his presidency was the Supreme Court decision in Marbury v Madison, which for the first time extended the power of judicial review to the judiciary.
https://millercenter.org/president/thomas-jefferson/key-events

https://www.monticello.org/thomas-jefferson/brief-biography-of-jefferson/

https://www.whitehouse.gov/about-the-white-house/presidents/thomas-jefferson/

The most important political development which took place during the Jefferson administration was the Louisiana Purchase.  The United States grew considerably after this purchase from Napoleon Bonaparte, and many in the United States were in favor of this expansion. Jefferson also sent a combined force of naval ships and Marines to defeat the Barbary Pirates—he considered this to be more cost-effective than constantly paying bribes.   
Jefferson's foreign policy was not altogether favorable, however.  Jefferson cut the size of the army and navy, and this would be detrimental during the War of 1812.  Jefferson feared that a strong military could be used to curtail the people's freedom.  To protest Britain and France stopping American cargo on the high seas, Jefferson passed the Embargo Act which prohibited trade with the two warring nations.  Unfortunately, the two nations were the United States' greatest trade partners, and the economy soon crashed. The losses were felt most acutely in New England.  Jefferson eventually lifted the Embargo Act, but New England, never a friend to Jefferson, was now more against the Virginian than ever before.