Adrienne Adams, the speaker of the New York City Council, entered the mayor’s race later than her rivals, but she is trying to prove in the final weeks of the campaign that she has the experience and temperament to become the city’s first female mayor.

Ms. Adams is running on a message of “no drama, no scandal — just competence and integrity,” offering herself as an alternative to Mayor Eric Adams and former Gov. Andrew M. Cuomo, both of whom were investigated for suspected wrongdoing.

Ms. Adams, who is not related to the mayor but did go to high school with him, recently qualified for $2 million in public matching funds and has a high-profile backer in Letitia James, the state attorney general. But the speaker still significantly trails Mr. Cuomo and Zohran Mamdani, a progressive state lawmaker, in the polls.

Ahead of the June 24 primary, the leading Democrats in the race visited The New York Times for interviews. We are publishing excerpts from those interviews, and this is the second in the series; our conversation has been edited for length and clarity.

We asked Ms. Adams, 64, questions about 10 themes, with the occasional follow-up, touching on her favorite book and whether she has regrets about how the city handled its outdoor dining program.

We’ve written previously about her proposal for guaranteed income, her clashes with the mayor and the loss of her father during the coronavirus pandemic.