The best book out there is still Quantum Computation and Quantum Information by Nielsen and Chuang. It isn't quite current, as it lacks both the advances in hardware (superconducting qubits) and algorithms (quantum/classical hybrids & the sampling benchmark that this article is talking about). It's still the best way to get started as it introduces everything from the linear algebra all the way up.

I work in quantum computing and it's the book I always recommend.

I have heard good things about Quantum Computing Since Democritus, by Scott Aaronson. I'm not sure how rigorous it is, though.

I found this blog post very informative. Obviously it doesn't have the content of a book, but it conveys a good first intuition of what quantum computing can and cannot do.

http://twistedoakstudios.com/blog/Post2644_grovers-quantum-s...

"Algorithms" by Sanjoy Dasgupta has a fantastic description of Shor's algorithm that uses a quantum Fourier transform to factor integers. I love this book. A great place to start.