In San Francisco, where start-ups dream of populating the world with self-driving cars and robots, another breed of company is aiming for riches this week: Levi Strauss & Company.

The maker of denim and Dockers, which traces its roots to the California Gold Rush, Levi’s will start trading on the public markets on Thursday for the second time in its 165-year history. The listing is a milestone for Levi’s, which has experienced a resurgence in the past decade, overhauling its image, operations and the stretch in its jeans to resonate with today’s shoppers who are increasingly disposed to athleisure wear.

Levi’s, some say, might even be cool again.

“It took them time but they’ve been able to restore a lot of brand equity,” said Marie Driscoll, a managing director who covers fashion and luxury at Coresight Research. “They have their authentic product that they’ve been making forever but adapted to what consumers want today.”

This week’s stock offering, which the company anticipates will raise more than $100 million, is an accomplishment for the chief executive, Charles V. Bergh, and highlights Levi’s ambitions to expand its apparel lines both in the United States and worldwide. Shares of the company are expected to sell for $14 to $16, which would value Levi’s between $5.4 billion and $6.2 billion.