I have just completed my first year study and know elementary analysis and a little bit functional analysis. I found that most of the ODE books just focus on calculation but no substantial explanation of theorems.Can someone suggest some ODE books which are from a more theoretical point of view?
A classical theoretical book on ODE is Hartman.
A very good book, and slightly less demanding than Hartman is Hale's book
ODE from a dynamical system theory point of view are presented in Wiggins' book
Update: Have no idea how, but I read that the question was about a second theoretical ODE course. For the first course in ODE none of the books that I mentioned (except Arnold's one) suits.
The best first theoretical book on ODE is, for my taste, is Hirsch and Smale.