Geoffrey Hinton's "Neural Networks for Machine Learning" on Coursera [0] is a pretty excellent course to cover the basics. There's a lot in the course, but if you just skim over the videos you'll get a pretty good "big picture" view of what's out there. As with any quantitive topic, it's best to take a first pass where you just glance at the math and come back later to really focus on the missing pieces

An important thing to realize is that much of deep learning is decades old neural networks research that has for one reason or another become more viable recently.