Getting into maths
One subject at a time, from linear algebra to Galois theory. Each stop leans on the ones before it.
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Linear algebra
Matrices as ways of moving space, and why the determinant is a volume.
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Group theory
Symmetry, and what happens when the order you do things in matters.
The problems end at $A_5$, the group that blocks a formula for the quintic.
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Galois theory
Why that group means there's no formula. Still being written.
Every subject has a start-here page, then the same three forms, so you can pick the one that suits how you learn.
What everyone asks is a guide built from the 2,000 most upvoted questions on Math Stack Exchange, in the order people get stuck. Thirty problems has no explanations at all, only problems and hints, and you prove the subject yourself. The field guide is a catalogue of the objects you'll meet, with the marks that tell look-alikes apart.