• Differential Equations
  Existence and uniqueness
  Fixed point stability, linear analysis, hyperbolicity
  Basic bifurcations: Saddle-Node, Transcritical, Pitchfork, Hopf, Homoclinic
  Conjugacy, Hartman-Grobman Theorem
  Conservative, Hamiltonian, Gradient, Reversible systems
  Liapunov Functions
  Limit sets, invariance, Limit cycles
  Poincare-Bendixson, Dulac Criteria, Index Theory
  Return Maps
  

• Maps (1-D)
  Fixed point stability, cobwebbing, hyperbolicity
  Periodic orbits, linear stability, eventual periodicity
  Logistic and Tent Maps
  Conjugacy
  Itineraries, Transition graphs, Liapunov exponents
  Sharkovskii Theorem
  Shift maps
  

• Maps (2-D)
  Linear Maps
  Fixed point stability, linear analysis, hyperbolicity
  Periodic orbits, Rotations
  
  

References:

Nonlinear Dynamics and Chaos, Steven H. Strogatz, Westview.
Chaos: An Introduction to Dynamical Systems, Kathleen T. Alligood, Tim D. Sauer and James A. Yorke, Springer.
Dynamics and Bifurcations, Jack K. Hale and Hüseyin Kocak, Springer.