No doubt, a very devoted and experienced teacher has been at work here, very much so to the benefit of beginners in the field of algebraic topology, instructors, and interested readers in general.

I’d like to go back and attempt to draw some sort of construction to illustrate the proof I mentioned for at least . The book is intended to help fill the gap (and another, more calculational, follow up to Concise is planned). Coming to the book, this is great starting point for Algebraic Topology if you know Point set Topology ( because he assumes that the reader knows Quotient Topology).Note: The superscript * denotes a missing solution, a partial solution, or a solution that’s wrong and has yet to be corrected. And I think it is indisputable that you simply will not be able to find a book that more richly and effectively conveys the intuitive geometric content of this subject. I'll list a couple I know about (I attended some of these courses), and I'll wiki this answer so people can add more.

But I wanted to know if anyone might have any advice for someone that wants to learn most efficiently/effectively when reading this book.

Hatcher's acolytes may counter that this is a book for mature students, so any gaps should be filled in by the reader along the way with pen and paper. For example, CW complexes have proved over time to be the most natural class of spaces for algebraic topology, so they are emphasized here much more than in the books of an earlier generation. I've since read or at least perused a handful of other books on the subject but none of them cover as much material as well as Hatcher does.