I have to read Allen Hatcher's textbook and I am having a really hard time with the book. To cite examples, I find chapter 0 unreadable, especially the bits about CW complexes (I feel that the proofs in chapter 0 are at best incomplete but I may be grossly mistaken) and also example 0.7 where he says that the three graphs are homotopy equivalent because they are deformation retract of a disk with two holes. Similarly, when I tried reading the proof of the Van Kampen's theorem, I felt the proof was not so clear with words like "perturb the vertical sides" making a cameo. In other words, I feel that the treatment is not rigorous.
Am I reading the book wrong? To clarify, this is not a rant against the book for the heck of it: I really want to try and read this book. I know that Hatcher's text is followed all over the world, so I am just trying to understand how to really read the book. Should I be spending a lot more time trying to fill in the gaps or am I supposed to gloss over the details? Thanks in advance for your suggestions!