The musical begins by introducing the main protagonist Alexander Hamilton and sets his background as coming from a poor family, his father having left and his mother dying when he was 12 years of age. By use of his intelligence and "top-notch brain", Alexander travels to New York, in the developing nation of America, in hopes for a better life ("Alexander Hamilton"). Upon arrival in the summer of 1776, he immediately seeks out the young upstart Aaron Burr for advice, who in turn tells him to "talk less, smile more" ("Aaron Burr, Sir"). Alexander instead joins up with three revolutionaries: John Laurens, Marquis de Lafayette, and Hercules Mulligan, and gains their friendship and trust in the Revolution by impressing them with his knowledge and skill ("My Shot"), and the four sing about earning their country by staking their lives for the cause (The Story of Tonight"). As news of the Revolution spreads and grows in excitement, the Schuyler sisters Angelica, Elizabeth, and Peggy Schuyler sing about their hopes and prospects of the Revolution.("The Schuyler Sisters")
The opposing Loyalist Samuel Seabury arrives and proclaims against the Revolution, while Hamilton defends the movement by opposing the Loyalist's actions ("Farmer Refuted"). A message then arrives from the king of England, King George III, explaining that the king will fight for the colonist's loyalty back ("You'll Be Back"). Despite this, Hamilton and his newfound allies go further to join the Continental Army, in which Hamilton is given and accepts a position as George Washington's right-hand man.
In the winter ball hosted by Philip Schuyler in 1780, the men are in attendance, and they set their sights on the three Schuyler sisters ("A Winter's Ball"). Elizabeth Schuyler, the middle Schuyler sister, immediately fancies Alexander, and after they are introduced by her sister Angelica Schuyler, they are married by the blessing of Eliza's father ("Helpless"). Angelica, however, still has feelings for Alexander, but keeps them aside for the sake of her sister ("Satisfied"). Aaron Burr then meets up with Hamilton, Marquis de Lafayette|Lafayette, John Laurens, and Hercules Mulligan, and privately admits to Hamilton that he is having an affair with the wife of a British officer. Hamilton tells him to go for her ("The Story of Tonight (Reprise)"). However, Burr explains that he will wait for what life has in store for him, like how he has waited for everything else in his past ("Wait For It").
As the Revolution is underway, Hamilton continually asks Washington for a promotion and for a command, to which Washington denies. George Washington instead promotes Charles Lee, which leads up to an incredibly distrastous battle, in which Lee is demoted to Marquis de Lafayette. Lee then proceeds to ridiculing Washington in public, which prompts Hamilton into taking action, which Washington forbids as it is increasingly likely to lead to a duel. Instead, Hamilton's close friend and Washington's aide-de-camp [John Laurens offers to duel Lee for him so he will not go against Washington ("Stay Alive"). Laurens wins the duel against Lee ("Ten Duel Commandments") but Washington comes to know about the duel and is outraged at Hamilton, consequentially sending him home to be with his wife Eliza ("Meet Me Inside"). Eliza tells Alexander that she is pregnant with his child, and although at first Hamilton is unsure of himself, Eliza assures him that he is everything to her and begs him to stay home ("That Would Be Enough").
As Marquis de Lafayette takes an increasingly powerful role in the development of the Revolution, he convinces France to aid the Continental Army, in which event shifts the balance to the Americans. However, he and Washington know that to win the battle they will need the help of Hamilton, and so Washington reluctantly calls Hamilton back to the army and gives him the command he has requested for so long ("Guns And Ships"). The night before the battle, Washington calls Hamilton aside and explains to him that no matter how big an impact someone has on the course of history, they cannot control how they are remembered in someone else's eyes ("History Has Its Eyes On You"). The Continental Army wins the battle after a British soldier surrenders to them ("Yorktown (The World Turned Upside Down)"). After their victory, King George III questions the colonists how they will set up government and tend their own nation and rule on their own without losing the people's trust ("What Comes Next?").
After the success in the Revolution, Hamilton returns home to his son Philip Hamilton, while Burr's daughter Theodosia is born; the two sing of their hopes and fears for the future ("Dear Theodosia"). After learning the shocking news of the death of John Laurens, Hamilton and Burr together travel to New York to complete their studies and return as lawyers. Due to his success, Hamilton is enlisted to a delegate of the Constitutional Convention in 1787. Hamilton privately requests Burr to write The Federalist Papers in defense of the new U.S. Constitution; however, after Burr's unmoving denial, Hamilton turned to James Madison and John Jay to write the papers. After Washington is elected in the Election of 1788, he gives Hamilton the opportunity to be the Secretary of the Treasury, and although Eliza pleads him not to accept the offer, Hamilton realizes how big of an opportunity it was and agrees ("Non-Stop").