What are the best books for understanding chaos theory and fractals?

[Newspeak]

I am looking for two different pairs of books. This first pair would be an introduction into the chaos theory and fractals(separate books). The second pair, I am looking for complete mathematical theory on each, preferably that is pretty self contained and in depth.

My background in mathematics is: Calc 1-3, Linear Alg., Diff. Eq., and Mathematical Physics. I will be taking Applications of Complex Variables, and PDE's.

I would also appreciate recommended math coverage for fractals.

 

[NoMoreExams]

I'm a strong believer that you can't do chaos theory without fully understanding dynamical systems, maybe others disagree. You might want to check out:

Light intro to Dynamical Systems and Chaos Theory: https://www.amazon.com/dp/0738204536/?tag=pfamazon01-20

Somewhat more in depth dynamical systems treatment: https://www.amazon.com/dp/0123497035/?tag=pfamazon01-20

Pretty in depth treatment (probably beginning graduate): https://www.amazon.com/dp/0521316502/?tag=pfamazon01-20