Modus ponens and tollens, relations, set theory and the ZF axioms, category theory and what mathematics stands on.
Groups and group actions, quotient groups, rings, fields, modules, polynomial rings and exterior algebras.
Vector spaces, linear operators and matrices, inner products, affine maps and tensors.
Number theory, Pythagoras, topology, combinatorics and dynamical systems.
The mathematics behind quantum mechanics and relativity.
Where to start: the general map of mathematics and its history and biography.