I am currently planning on self studying Non-linear dynamics, with an intention of developing a decent idea about it and see how its applied. I don't want to be too rigorous in my dealing with the subject right now. I have just completed my first year as an MSc Physics student, so what are the books that would be good, at this level.
Strogatz's Nonlinear Dynamics and Chaos is a very friendly introduction to the subject, and is written in a very intuitive way. Personally I like the fact that gives you a very broad idea of the subject, without going into many unnecessary details. For a first approach to NL dynamics I strongly recommend this book.
If you are motivated by the subject and want to delve into the problems that make it fascinating, you can try The Chaos Book. This is an open resource written by Cvitanovic, one of the greatest in the field. You can approach this book in many different ways, is a good reference book, it is also great book for medium/advanced readers, but the amazing part is that you can get a lot from it if you are just a beginner. If you decide to go for this book, I strongly recommend to solve the problems!