Book Searching in Stability Theory. Can anyone recommend me a book on Stability Theory with an intuitive approach? 
I have some course notes on that subject, but it's really abstract and theoretical. I really want to understand it, ex: 
Stable by Lyapunov/Asymptotically Stable/Globally Asymptotically Stable/  Lyapunov's Stability Theorem/ Hurwitz criteria...
If there are many exercises (Or examples) with instructions in books which are wonderful for me.
Any suggestions about titles and authors's books (free download :) ) or pdf/djvu file, it will be appreciated. Thanks!
 A: Strogatz - Nonlinear Dynamics and Chaos
A: Your question is not easy to answer, so you might want to check these out on your favorite book site to see if they suit your needs. A book that one person likes, may be awful for the next person, so it is difficult to gauge how much mileage you will get from these recommendations.
They should also provide guidance for other similar books.


*

*The Qualitative Theory of Ordinary Differential Equations, Brauer and Nohel

*Modern Control Theory, Brogan

*Problem Solver in Automatic Control Systems / Robotics, REA (has worked examples)

*Design of Feedback Control Systems, Hostetter, Savant, Stefani

*Stability Theory of Differential Equations, Bellman


As for free, sorry, cannot help you there, but there is a lot of material in these areas on the web.
You might also consider seeing if there is Open Courseware (like MIT) in these areas as that is always helpful.
A: Paul Glendinning, Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations. Intuititive, not bogged down in technical details (of type 'should this be $C^2$ of $C^{1,\alpha}$?...'), & quite modern. Of course, I think you would also benefit from consulting such classics as Jack Hale's ODE book or the Coddington-Levinson one, as generations of other students did.
A: I like the book written by Jorge Sotomayor. 
Teoria Qualitativa das Equações Diferenciais. 
Thats a good one!
Or 
Perko L. Differential equations and dynamical systems (Springer, 1991)(K)(T)(208s)
A: U can check the following Books: NonLinear Differential Equations and Dynamical Systems Second edition ---- By Ferdinand Verhulst 
Or get J. Cronin O.D.E (Introduction and qualitative Theory)
Best Of luck
