Mikko Nissinen, the artistic director of Boston Ballet whom we affectionately refer to as “the Flying Finn,” will be sticking around for a while. Nissinen has just renewed his contract with the company, inking a deal that will keep him here for another five years. The Helsinki native started his dance training at the Finnish National Ballet School before turning pro at the age of 15 with the Finnish National Ballet. He became Boston Ballet’s artistic director in 2001, cultivating a repertoire that ranges from classical — Petipa’s “The Sleeping Beauty,” Nureyev’s “Don Quixote,” and Bournonville’s “La Sylphide” — to contemporary, including works by William Forsythe, Jiri Kylián, Peter Martins, and Mark Morris. “I look at the next five years and we already have a clear idea of exciting things for Boston,” said Nissinen, reached Friday as he boarded a flight to Oslo to see a new version of “Swan Lake.” “We have to curate the past, stay relevant to today’s people, and pave the way into the future. . . . I’m having a grand time and Boston Ballet has amazing momentum at the moment.” Judging from the crowd of 55,000 people that gathered on Boston Common last fall to see the company celebrate its 50th season, he’s right.