Aaron Burr opens the show with the line, "How does a bastard, orphan, son of a whore/And a Scotsman, dropped in the middle of a forgotten spot in the Caribbean by providence impoverished,/In squalor, grow up to be a hero and a scholar?" Various characters take turns telling the audience about Hamilton’s childhood in the Caribbean in a song called "Alexander Hamilton," detailing the hurricane that destroyed his town, his father's abandonment of him, his mother's death, and his cousin's suicide. None of these adversities discouraged Hamilton from working hard in order to make his way, working for his mother's landlord and eventually making his way to America. In this opening song, all of the main characters are introduced, and we learn what their role in the story will be: Lafayette and Jefferson, Mulligan and Madison, who fought with or against him; Laurens and Philip, who died in war or dueling; Washington, who trusted him as his right-hand man; and Eliza, Angelica, and Maria, who loved or lusted after him. Aaron Burr comes back and concludes the song, admitting to the audience that he is the one who shot Hamilton, foreshadowing the end of the story.
The scene cuts to 1776, New York City. Hamilton introduces himself to Burr in order to ask for advice on how to graduate from college quickly (Burr graduated in 2 years) and join in fighting the Revolutionary War. He admits that he punched the bursar of the college (a friend of Burr's) when the bursar looked at him like he was stupid. When Hamilton asks Burr how he graduated so quickly, Burr tells him that it was his "parents' dying wish," and Hamilton feels kindred with him because they are both orphans. Burr advises him to "talk less, smile more, don’t let them know what you're against or what you're for," and invites him to go have a drink. Hamilton cannot believe that Burr has such a strategic outlook on life, and follows him to the bar.
The characters Laurens, Lafayette, and Mulligan enter the stage rapping loudly and sit around a table at the bar. When they see Burr they ask him to tell them his thoughts on the revolution. Burr laughs and tells them that they are taking too many risks; he would rather stick to the sidelines for the moment. The others aren’t happy about this, but before they can say much Hamilton tells Burr that he should be able to fight and die for something—otherwise, what's the point of life?
The men are surprised by Hamilton's passionate stance, and he launches into his own number called "My Shot" about how he doesn't want to take his life for granted. In the course of the song we discover that he is very poor and he is living a humble life. Hamilton also reveals his desire to fight in order to free his country from England's colonial rule. The other three introduce themselves and their ideals. Lafayette is a Frenchman who wishes to take down the monarchy in his own country, as well as help the American colonies shake off England. Mulligan is a tailor who is sick of his position and wishes to advance socially using the revolution. Laurens is an abolitionist who dreams of forming the first all-black battalion, as well as helping bring an end to slavery. Burr cuts in here, telling them that although he agrees with their cause, he thinks they are far too reckless. Hamilton forms a friendship with the three new characters, singing with Laurens about rising up and taking back their country with the help of the people. His three new friends want to put him "in front of a crowd," and everyone in the bar bursts into song and dance. Hamilton expresses his fear of dying without a legacy or a cause.
The new friends toast to their shared cause and sing "The Story of Tonight," about how people will tell their story in the future.
Suddenly, Aaron Burr enters and introduces us to the wealthy Schuyler sisters. Eliza, Angelica, and Peggy have traveled to see the revolution "happening in New York." Peggy, the youngest, is worried that their father would not approve of them being there and tries, unsuccessfully, to convince her sisters to leave. Meanwhile, Eliza and Angelica are enthralled by the revolution taking place in the city. Burr tries to flirt with Angelica, who clearly knows him and is unimpressed. She tells him that although they may want a revolution, she is more interested in women receiving equal rights. She expresses her desire to fight with words rather than with weapons.
Hamilton, spurred on by his friends, engages in a verbal battle with Samuel Seabury, a man preaching support of the King. Seabury is not as quick thinking or witty as Hamilton and can only repeat his prepared speech, of which Hamilton quickly twists the words in a counter argument, singing with and over him to do so. The ensemble interrupts this dispute, alerting the assembled people to a message from King George.
King George enters as a visual representation of his letter, informing the citizens of America that he will fight to keep the country as his own and that he is not worried that they will defeat him. In "You'll Be Back," a parody of a love song, he tells his American subjects that he loves them. In the course of the song, George threatens to send an army to keep them in line, but his threats are masked with a friendly and loving tone.
The scene shifts to the revolution, and the changing political tides. Hamilton and Burr introduce George Washington and describe the part he plays in the revolution. Washington complains that his troops are disorganized and will not stop retreating. He knows that the odds are against him and they need someone who can organize and strategize if they hope to win. Hamilton, in the meantime, is taking his own initiative and stealing canons from the British to further the American cause. Burr enters and tries to sell himself to Washington but ends up insulting him and his tactics, so Washington tells him to leave just as Hamilton enters. Washington wants Hamilton as his righthand man, as he has heard about his skills and quick wit. Hamilton is conflicted, as he wants to command troops, not write or work in politics.
The soldiers take part in a ball, where Burrs tells Hamilton that the quickest way to money is to marry one of the rich Schuyler sisters. Eliza Schuyler takes the spotlight as she sings about falling for Hamilton. They dance together and exchange letters for a couple weeks, after which Hamilton asks Eliza's father for his blessing in marrying his daughter. The two marry and the line "in New York you can be a new man" repeats from the first song, making it clear that Hamilton has reached a turning point in his life.
Unsurprisingly, as a musical, Hamilton uses songs and musical numbers to tell the story of Founding Father Alexander Hamilton. A rousing song opens the musical, with a slew of different supporting characters helping to introduce the titular protagonist. Not only is the use of music integral to the piece, but also the fact that the music is an amalgamation of traditional melodic musical styles and American popular music, specifically hip-hop and rap. The characters rap their way through the opening number, spinning rhymes out of the biographical information about Hamilton and bringing what might otherwise seem like dry exposition to vibrant life.
The use of rap music in a Broadway musical is anachronistic enough, as traditional American musicals do not usually use rap styles in their scores; additionally, the rapping is all the more anachronistic because Hamilton is a story that takes place in the 18th century, and concerns the Founding Fathers of the United States. The Founding Fathers were a group of powdered-wig-wearing white men looking to cash in on some new land. Hamilton is all the more daring because instead of pairing these characters with a courtly classical music that might fit in better with the setting, it takes its inspiration from black vernacular music, and the cast is comprised of mostly non-white actors, who rap their way through a story that one might expect would be given a much more staid treatment. The contrast between the style of the show and its subject matter is apparent from the start and lends it a unique and exciting quality.
From early on, a notable contrast is established between the temperaments of Hamilton and Burr. While Hamilton has a fiery temper, a gift for rousing rhetoric, and a passionate political point of view, Burr is more measured, strategic, and subtle in his opinions. When they first meet, Butt counsels Hamilton to be less hot-headed, to talk less, and to keep a lower profile, but Hamilton feels unable to do so. Later on, these differences in temperament have profound effects on each man's destiny, with Hamilton's approach proving more successful and helpful to the revolution. What begins as a subtle difference in attitude grows into a more pronounced rivalry between the men.
Hamilton's song "My Shot" is both a traditional "I want" song in line with musical theater conventions—a song which explicates the protagonist's desires and goals—as well as a traditional rap song, complete with bravado and intricate wordplay and rhyming. The song's crossover elements typify the overwhelming popularity and mass appeal of the musical. In blending two seemingly disparate styles—musical theater and rap—and fusing them through an anachronistic investigation of American history, writer and star Lin-Manuel Miranda shows viewers the commonalities and convergences of different ideas, and creates an image of cultural interconnectedness.
The styles of the various songs reflect broader structures in the plot. For instance, in contrast to the rap flow of most of the score, the villainous King George's music fits into a more traditional musical convention. His vocally impressive and more studied musical number show that the King and England is very much out of step with the "young, scrappy, and hungry" American revolutionaries. Where they are invested in freedom and revolution, he maintains a mannered bearing, with a threatening tremor of violence (however comic) resting just beneath the surface.