I am interested in the field of Quantum computer/Quantum computing. with which books I should start, and what are the 'must read' books in this domain?
This book is very extensive and covers a lot of material. It's great as a first read -- provided you are familiar with quantum mechanics (you will not need quantum field theory, in case you were wondering). Another great book, but less familiar, is by Kitaev, Shen and Vyalvi:
This book goes beyond that of Nielsen and Chuang and is more aimed at mathematical rigor. I would not recommend it as a first read, but it's worth going through at a later stage.
See also this website by John Preskill and his course on Quantum Computing: