I am a first year graduate student in math. I am taking a graduate course on ODE which covers the topics listed below. I feel that the lecture notes of my instructor are great. However, like with any math course, there is no way for me to have a full understanding of the topic without solving problems on each topic. I really appreciate if anyone can tell me about a good textbook that has lots of solved examples/problems about all/some of the topics listed below so that I can go over all these problems/examples to "master" the material. I also included at the end of this post a bit about my background so that you list only books that I can read. Thanks in advance to anyone who answers this post!
Chapter 2: Linear Systems:
Chapter 3: Stability: Basic theory
Chapter 4: 4. Nonlinear Systems: Local Theory
Chapter 5: Nonlinear Systems: Global Theory
Chapter 6: Bifurcations