Here is a list of The Vorkosigan Saga Books in Publication Order.
This series was not written with an internal chronology, so this is a list of the publication order. However, the author, Lous McMaster Bujold suggests this reading order.
#1 – Shards of Honour (1986)
From the blurb:
When Cordelia Naismith and her survey crew are attacked by a renegade group from Barrayar, she is taken prisoner by Aral Vorkosigan, commander of the Barrayan ship that has been taken over by an ambitious and ruthless crew member. Aral and Cordelia survive countless mishaps while their mutual admiration and even stronger feelings emerge. A science fiction romance by a Hugo and Nebula Award winning master. Bujold’s SHARDS OF HONOR is the first book in her SF universe to feature the Vorkosigan clan, followed by the Hugo award-winning BARRAYAR. The Nebula award-winning FALLING FREE precedes it by internal chronology in the same future history.…