- Mark Beck, *Quantum Mechanics: Theory and Experiment*, might be the best QM book there is. The math needed is modest, but knowledge of optics and electromagnetic waves is almost necessary. 

You can also try two simpler, very short books by Valerio Scarani (aimed at, mainly, high school students), 

 - *Quantum Physics: A First Encounter: Interference, Entanglement, and Reality* 
 - *Six Quantum Pieces: A First Course in Quantum Physics*. 

All three books are modern: instead of stressing (otherwise free) particle(s) in a box and the Bohr's atom, they emphasize one particle interference, entanglement, local realism, quantum teleportation. Dr. Beck's book describes quantum optics labs that his undergraduate students really performed, to test single-photon interference, violation of local realism, etc. 

Another modern book is 

 - *Exploring the Quantum* by Serge Haroche and Jean-Michel Raimond. 

It's at about the difficulty level of Mark Beck's book, but much cheaper when buying it used. Similar to Valerio Scarani's books are 

 - *Dance of the photons* by Anton Zeilinger, and 
 - *Quantum Enigma* by Bruce Rosenblum and Fred Kuttner. 

Note that all the above authors are well known professors and/or researchers.