I am quite new to the forum so please feel free to correct/give pointers if I am posting something in the wrong place.

I have been perusing "Dimension Theory" by Witold Hurewicz & Henry Wallman and while doing so noticed I couldn't quite see the reason for 'studying/researching' dimension theory. As an undergraduate when I was taught the concept of dimension in terms of 'linear independence' and 'spanning' of vectors I never paid much heed to alternate/analytical formulations of dimension. Now having come across, say, the Hausdorff, Fractal, Assouad dimensions I am quite curious as to why mathematicians have focussed so much on this avenue. 

I would be very, very grateful for any pointers or links which can give me a little bit of 'general' motivation for studying dimensions i.e why study dimension theory. Specific examples from dynamical systems, metric geometry, number theory, set theory et cetera are very welcome too. 

Thank you, thanks a lot!

P.S the tags might be a little over the place - couldn't quite create new ones for metric geometry and assouad dimension.