This series started as Legion of Super-Heroes (2005-2006) and then changed its title to Supergirl and the Legion of Super-Heroes in issue #16. Supergirl appeared from issues #16-36, which were collected in four volumes . The series continued under the original title after Supergirl’s departure, finishing with issue #50. The post-Supergirl issues were not well received due to the change in creative team.
In-universe, Supergirl travelled to the 31st century between Supergirl #5 and #6 of her 2005 series, however this was never referenced in her own series until she regained her memories in Supergirl #21-22 when she encountered an alternate version of the Legionnaires in her own time. This series stands on its own very well without requiring any knowledge of the contemporary DCU continuity. Although Supergirl does not appear in the first two volumes, they are recommended reading for future volumes.
Legion of Super-Heroes Vol. 1: Teenage Revolution
Available at digital bookstores. Collects issues #1-6 and and the preview story from Teen Titans/Legion Special #1. Supergirl does not appear.
Legion of Super-Heroes Vol. 2: Death of a Dream
Available at digital bookstores. Collects issues #7-13. Supergirl does not appear.
Supergirl & the Legion of Super-Heroes Vol. 3: Strange Visitor From Another Century
Collects Legion of Super-Heroes #14 and Supergirl and the Legion of Super-Heroes #16-19, and the letter column back-ups from Legion of Super-Heroes #6, 9, 13-15. Does not include issue #15 (available on Comixology).
The 21st Century’s Girl of Steel wakes up 1,001 years later, convinced the whole reality is something she just dreamed up.
Written by Mark Waid and Tony Bedard; Art by Barry Kitson, Adam DeKraker and Mick Gray.
Supergirl & the Legion of Super-Heroes Vol. 4: Adult Education
Collects issues #20-25
Written by Mark Waid and Tony Bedard; Art by Barry Kitson, Mick Gray and various.
Supergirl & the Legion of Super-Heroes Vol. 5: The Dominator War
Collects issues #26-30
Written by Mark Waid; Art by Barry Kitson and Kalman Andrasofszky; Cover by Kitson.
Supergirl & the Legion of Super-Heroes: The Quest for Cosmic Boy
Collects issues #30-36
Written by Tony Bedard ; Art by Kevin Sharpe and Dennis Calero ; Cover by Barry Kitson.