Basically, Ana as a child witnesses her father & little brother being murdered by an upstart Yakuza boss. She is raised catholic by her mother w/ forgive & forget values but raised as a Sohei warrior by her grandfather to avenge the family honor. Jump to current day NYC & she comes to America under the guise as a Japanese art dealer w/ the sole purpose of bringing down said yakuza boss who has now brought his operation to America under the umbrella of Japanese business corporation. Ana begins her quest to bring down the Yakuza boss by bringing down his entire foundation. Turning Mafia against yakuza against bad cops etc. The story takes several twists & turns thru love, foiling plans, Ana's best friend (who belongs to a centuries old rival Sohei sect) to kill her, boyfriend cop losing his badge, etc. Eventually, when the time comes to fight her enemy one on one, the ending takes yet another surprising twist. Later on, all the killing has caught the attention of her grandfathers peers in Japan & they order her dead, capturing her mother & using her as bait against Ana. The rescue attempt results in Ana's capture & she as well as her mother are sentenced to death. Just when all looked lost, a rogue group from w/in the Kyoto Sohei who were inspired by her actions set her free to fight for her life. Next, she is betrayed by her best friend from the Nara Sohei sect who not only attacks Ana's enemies, but her saviors as well. Ana's grandfather appears just in time to take out the leader of the Kyoto Sect who lead the capture of Ana & her mother.
That should be enough of a description for now.
SHI: Way of the Warrior 1-12
SHI vs Tomoe
SHI: Tora No Shi 1-3
SHI: Heaven & Earth 1-4
from there, the sidebars to the story go nuts.
I recommend staying away from Shi: The Series until after you read the base story.