Can you spoil history?
The show is in lots of ways built around those three duels, which makes sense given that the elephant in the room of any story about Hamilton and Burr is their ultimate duel.
The first duel, in December of 1778, is between Laurens and Charles Lee, who was challenged by Laurens for running down General Washington's leadership after being relieved of command for his failure at Monmouth. What makes this an inescapable part of the show, IMO, is that Hamilton was Laurens' second and Burr was Lee's. (Charles Lee took a bullet in the duel, but it wasn't apparently serious -- he lived until 1782, and probably died of tuberculosis.)
The second, famously, was between Hamilton's son and George Eacker, in 1801. (Eacker, too, died of TB, in 1804.)
Obviously, the final one was between Hamilton and Burr, in the summer of 1804.