Topology is just the study of topological spaces and how their properties are preserved under homeomorphisms. If you want to learn more you can purchase my textbook for 899.99$
Well before you continue I believe it is very important to adress the motivation of studying topology.
>We all know that topological spaces are transformed using continuous maps.
>Of course we know that continous maps are arrows in the category of topological spaces.
>Obviously we known that we need arrows to understand functors.
>Of course we need functors to understand natural transformations.
>We need natural transformations to understand adjoint functors
Now that everybody is motivated we may now begin the first course:
THEOREM 1.1:
Every simply connected,closed 3-manifold is homeomorphic to the 3-sphere.

PROOF:
>See exercise 1.1

EXERCISE 1.1:
The proof is trivial and left to the reader as exercise.