The election of 1800 was a rematch of the election of 1796, it was John Adams versus Thomas Jefferson.
Thomas Jefferson beats John Adams with 73 electoral votes, but his running partner, Aaron Burr, also got 73 electoral votes.
I choose Jefferson!
The decision then goes to the house which puts Alexander Hamilton in charge of making the decison and he chooses Jefferson because he despises Burr.
Before Jefferson takes office John Adams fills all positions with federalist judges and appoints William Marbury the last night hes in office, so Jefferson tells James Madison not to deliver the papers to Marbury until the next day, so Marbury sues Madison.
Thomas Jefferson was officially announced the 3rd president of the United States and Burr the vice president.
The case of Marbury vs Madison goes on and the court rules in favor of Madison and this case establishes the power of judicial reveiw.