Alexander Hall was first proposed in 1890, when the trustees determined that Princeton needed a convocation hall that could seat the entire student body for commencement and other large gatherings. Harriet Crocker Alexander donated the money for such a building to be named in honor of her husband Charles B. Alexander (Class of 1870), his father Henry M. Alexander (Class of 1840 and a College trustee), and his grandfather Reverend Dr. Archibald Alexander (Class of 1810 and founder of the Princeton Theological Seminary).

Construction on Alexander Hall began in 1892 and was completed two years later. During its early years, Alexander Hall was used for many lectures, mass meetings, and various assemblies, such as the events at the 150th anniversary celebration and Woodrow Wilson's inauguration as University President. For 30 years, freshmen were welcomed and seniors graduated in Alexander, but by 1922 commencement exercises had outgrown the building and thereafter were held in front of Nassau Hall. When the University's Marquand Chapel burned in 1920, Alexander was used for religious services until the new University Chapel was completed in 1928.

In 1984-85, Alexander Hall was extensively renovated and renamed as a result of a major gift to a Campaign for Princeton from David A. Richardson '66 in memory of his father, David B. Richardson '33. The elder Richardson, a lifelong enthusiast of classical music and a successful lawyer and investor, died in 1980. This project revitalized the building for use as an 891-seat concert hall. Buddy Graham, winner of six Grammys and one of the most highly regarded engineers for symphonic recording in the late twentieth century, listed Richardson Auditorium in the company of Carnegie Hall and the Concertgebouw in Holland as one of the world's acoustically "great" concert halls.

(Adapted from Richardson History and Architecture.)