The topic is "Control Theory." The author's book "Applied Control Theory for Embedded Systems" may be a useful addition if you're going to apply this stuff. I found the book helpful, but I personally didn't find it as clear and easy to read as "PID Without a PhD".
PID control is probably what you'll see in an introductory undergraduate engineering control theory course (which I haven't taken). I think you'd typically study the dynamics using numerical simulation and Laplace transforms. You might think about making a practical project (I made a PID reflow oven controller).
After that you're off to the races with State Space methods (e.g. Chen's "Linear System Theory and Design".) and you can think about problems like stabilizing a quadrocopter based on inertial measurements.
