The Princeton Companion to Mathematics

Something else I’ve found extremely useful in getting into maths topics is the Princeton Companion to Mathematics - it doesn’t have exercises but gives excellent overview essays of a wide range of maths topics - expensive to buy (mine was a present) but should be available in academic libraries, say. https://www.amazon.co.uk/Princeton-Companion-Mathematics-Tim... (https://www.amazon.co.uk/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809)

It's easy to gain physical intuition because you can often explain one physical phenomenon in terms of another physical phenomenon that you have much more real life experience with. But with mathematics, "intuitive" analogies are all in terms of other mathematical objects! You can't build intuition if you don't even know what they trying to abstract over. In that regards, The Princeton Companion to Mathematics is fantastic because it maps out how the different fields of mathematics are interrelated.