In no specific order:
- Alligood K.T., Sauer T.D., Yorke J.A, Chaos. An Introduction to Dynamical Systems
That's a personal favorite of mine at the undergraduate level. It's clearly written and they strike a great physics/math balance, including from (a few) mathematical proofs to "computer experiments".
- Tél T., Gruiz M., Chaotic dynamics. An introduction based on classical mechanics
Highly recommended. Also aimed the the undergraduate level, it's very clear conceptually and strives to make the math accessible. It's a newer book (2006) that includes current topics.
- Ott E., Chaos in Dynamical Systems
A classic that cannot be missed. It's aimed at the graduate level, but it's pretty accessible and especially useful when you need to get to the details of some specific topic.
- Strogatz S.H., Nonlinear Dynamics And Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
It's explicitly aimed at newcomers and has only calculus and introductory physics as prerequisites. The title "applications" include "love affairs" as 2-D flows and, possibly very interesting, the author lectures are available on Youtube.
- Cvitanović P., Artuso R., Mainieri R., Tanner G., and Vattay G., Chaos: Classical and Quantum $-$ ChaosBook.org
That's a very interesting freely available on-line graduate textbook. It takes a fresh approach to the subject and "aims to bridge the gap between the physics and mathematics dynamical systems literature".