Steven H. Strogatz: Nonlinear Dynamics and Chaos (Addison-Wesley 1994). Introduction to flows, fixed points, manifolds, bifurcations. Students like the book.

K.T. Alligood, T.D. Sauer and J.A. Yorke, Chaos, an Introduction to Dynamical Systems (Springer, New York 1996). An elegant introduction to maps, chaos, period doubling, symbolic dynamics, fractals, dimensions. A good companion to this webbook.

E. Ott, Chaos in Dynamical Systems (Cambridge, 1993). As above, with baker's map used to illustrate many key techniques in analysis of chaotic systems. Perhaps harder than the above two as the first book on nonlinear dynamics.

For examples, check introductory course homepages.

The introductory course should give students skills in qualitative and numerical analysis of dynamical systems for short times (fixed points, bifurcations) and familiarize them with Cantor sets and symbolic dynamics for chaotic dynamics. With this, and graduate level exposure to statistical mechanics, partial differential equations and quantum mechanics, the stage is set for any of the 1-semester advanced courses based on this webbook. Each course starts with the introductory chapters on qualitative dynamics, symbolic dynamics and flows.

Deterministic chaos : Chaotic averaging, evolution operators, trace formulas, zeta functions, cycle expansions, Lyapunov exponents, billiards, transport coefficients, thermodynamic formalism, period doubling, renormalization operators.

Spatiotemporal dynamical systems : partial differential equations for dissipative systems, weak amplitude expansions, normal forms, symmetries and bifurcations, pseudospectral methods, spatiotemporal chaos.

Quantum Chaology : Semiclassical propagators, density of states, Gutzwiller trace formula, semiclassical spectral determinants, billiards, semiclassical helium, diffraction, creeping, tunneling, higher h-bar corrections.