Yanofsky and Manucci's "Quantum Computing for Computer Scientists" is a smooth intro if you come from a CS background. Nielsen and Chuang's "Quantum Computatio

Yanofsky and Manucci's "Quantum Computing for Computer Scientists" is a smooth intro if you come from a CS background. Nielsen and Chuang's "Quantum Computation and Quantum Information" is more thorough and advanced from a mathematical point of view. But it contains a primer on the linear algebra required.