The series takes place four years after the events of Mahou Shoujo Lyrical Nanoha StrikerS, during which Nanoha Takamachi rescued and adopted a young girl named Vivio, who is the reincarnation of the Sankt Kaiser, Olivie Segbrecht. After entering her fourth year of elementary school, Vivio is given her own intelligence device, Sacred Heart, and gains the power to transform using her adult Sankt Kaiser mode. She soon comes across a girl named Einhart Stratos who, similar to Vivio, is the descendant of another Sankt Kaiser ruler, Claus G.S. Ingvalt. As Einhart becomes determined to prove her fighting style is the strongest, Vivio befriends her and, together with her friends, enters a martial arts tournament where they fight against various opponents and learn more about their past lives.
 
Included one-shot: 
Volume 2: 5th Anniversary Collaboration Comic: Fate/stay night x Mahou Shoujo Lyrical Nanoha

The manga takes place four years after the JS incident in Magical Girl Lyrical Nanoha StrikerS, and stars Vivio Takamichi, a fourth-year elementary student at St. Hilde Academy of Magic. Vivio has learned to conjure her adult form and has received her own Device — named Sacred Heart — from Nanoha, and has promised Nanoha to never use either for mischief. Then a mysterious magical fighter appears and targets Vivio.
 
(Source: Anime News Network)

Chapters 1-3 are the events that occurred between the end of A's and the start of StrikerS. 
Chapters 4-12 are side stories about the characters. 
Chapters 13 &amp; 14 are the events that occurred after the end of StrikerS. 
Chapter 15 is a special from Megami September 2009 (also events after the end of StrikerS).

The story appears to be centered on the investigation of the Book of the Silver Cross, an ancient Belkan magical tome. Tohma Avenir, whilst traveling, discovers a girl named Lily Strosek trapped inside a construct. When rescuing her, she gives Tohma an amulet that gives him access to a new Device power. However, unbeknown to them, there is another with a similar Device causing massive damage and injury, leading to an investigation by the Time Space Administration Bureau.

4-koma of Mahou Shoujo Lyrical Nanoha Vivid.

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