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

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The discussion centers on finding two pairs of books: one pair for introductory material on chaos theory and fractals, and another for comprehensive mathematical theories on these subjects. The individual has a solid mathematical background, including calculus, linear algebra, differential equations, and mathematical physics, and is preparing to study complex variables and partial differential equations. There is a strong emphasis on the importance of understanding dynamical systems as a foundation for chaos theory, with recommendations for introductory and more advanced texts on dynamical systems and chaos theory provided, highlighting various levels of depth suitable for different learning stages.
Newspeak
I am looking for two different pairs of books. This first pair would be an introduction into the chaos theory and fractals(seperate 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.
 
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