It launched the crew of the visiting mission ISS EP-1, which included the first paying space tourist Dennis Tito, as well as two Russian cosmonauts.

TM-32 carried a three-man crew (two Russians and one American, the latter not a professional astronaut) to the International Space Station, ISS.

It docked automatically with the ISS at 07:57 UT on April 30, 2001, just a few hours after the space shuttle Endeavour on mission STS-100 undocked.

The launched crew stayed for a week and returned in Soyuz TM-31, which had been docked to (or nearby) the station since November 2000 functioning as "lifeboat" for the onboard crew (Expedition 1 and 2).

As the new lifeboat for Expedition 2 and later Expedition 3, TM-32 stayed docked at the station for six months (except for a brief move between docking ports) and finally, on October 31, brought home two cosmonauts and an ESA astronaut who had arrived a week earlier in Soyuz TM-33.