I’m not throwin’ away my shot.

Hey yo, I’m just like my country.

I’m young, scrappy and hungry.

That verbal fusillade delivered by Lin-Manuel Miranda, playing Alexander Hamilton, began the sensational performance of Mr. Miranda’s project, “The Hamilton Mixtape,” on Wednesday evening at the Allen Room, where it opened the new season of Lincoln Center’s American Songbook series....

Who would have thought of comparing America’s founding fathers to contemporary rappers? But “The Hamilton Mixtape,” inspired by Ron Chernow’s biography of Hamilton, finds him furiously quarreling with Thomas Jefferson (Jon Rua), James Madison (James Monroe Iglehart), and Aaron Burr (Utkarsh Ambudkar), in cabinet debates moderated by George Washington (Christopher Jackson)....