Without knowing any specifics I would say the most universally useful tool to have in your nonlinear controls belt is Lyapunov control design and its extensions (if you're familiar with Lyapunov equations in linear systems that's where the connection starts). It leads to useful methods that are applicable to many systems, and allows you to handle some particularly tricky situations. Wikipedia's articles on these topics are surprisingly decent:
https://en.wikipedia.org/wiki/Control-Lyapunov_functionhttps://en.wikipedia.org/wiki/Backstepping
as well as Stanford's lecture notes:
https://web.stanford.edu/class/ee363/lectures/lyap.pdf
Check out Robust Nonlinear Control Design by Freeman and Kokotovic for more on this.
Compared to linear control theory, nonlinear controls is much more fractured and domain-specific. No concept is as widely applicable as ones from linear controls. Khalil's Nonlinear Systems book is generally considered a top reference, but it does start to get into the PhD-level stuff and I don't recommend it to a non-specialist unless you are really into this stuff. I can give more specific recommendations if you have a particular industry or application in mind.
Compared to linear control theory, nonlinear controls is much more fractured and domain-specific. No concept is as widely applicable as ones from linear controls. Khalil's Nonlinear Systems book is generally considered a top reference, but it does start to get into the PhD-level stuff and I don't recommend it to a non-specialist unless you are really into this stuff. I can give more specific recommendations if you have a particular industry or application in mind.