Winkler's audition for the Yale School of Drama was to be a Shakespeare monologue, which he promptly forgot, so he made up his own Shakespeare monologue. Out of a class of 25 actors, 11 finished. During summers, he and his classmates opened a summer stock theater called New Haven Free Theater, putting on various plays including Woyzeck, and an improv night. The company put on a production of The American Pig at the Joseph Papp Public Theater for the New York Shakespeare Festival in New York City. In June 1970, after graduating from Yale, Winkler was asked to be part of the Yale Repertory Theatre company, which included James Naughton and Jill Eikenberry. During his time there, Cliff Robertson, who had seen him perform in East Hampton, offered him a part in his film The Great Northfield Minnesota Raid. Winkler had to decline because he had no understudy for his current role, and thus was unable to leave. He stayed with the Yale Repertory Theatre for a year and a half. In 1971, Winkler got a job at the Arena Stage in Washington, D.C. to work on the play, Moonchildren, but was fired by director, Alan Schneider. In 1977, Winkler appeared in a TV special, "Henry Winkler Meets William Shakespeare," part of the CBS Festival of Lively Arts for Young People instructional series for children. With the assistance of Tom Aldredge as Shakespeare, Winkler, as himself, introduced an audience of children to Romeo and Juliet, The Taming of the Shrew, Hamlet, and Henry IV and explained to them how Shakespeare's plays were produced at the Globe Theatre in London in the 17th century. He also played Romeo in the scene from Romeo and Juliet in which Romeo slays Tybalt in a sword duel.

Answer this question "What plays did he do with the Yale Repertory Theatre?" by extracting the answer from the text above.
During his time there, Cliff Robertson, who had seen him perform in East Hampton, offered him a part in his film The Great Northfield Minnesota Raid.