Many students have an understanding of the simple vector model to describe NMR experiments (if you don't you should take CHM 4380/8309B). The vector model can only explain the simplest of pulse sequences. To explain more complex sequences such as COSY, HMQC etc... one must resort to more involved models such as product operators. If you want to understand your NMR experiments I highly recommend the following book:
Understanding NMR Spectroscopy by James Keeler (Wiley, 2005)
You can also download notes from this book from the following web site:
This is by far the best textbook I have seen on high resolution NMR spectroscopy since the early 1980's. It is written on a senior undergraduate level and very understandable.