3 +

study presentations, zum beispiel:

$\langle a,b\mid a^2=b^3=e, ab=b^2a \rangle$

vs

$\langle a,b\mid a^2=b^3=e, ab=ba \rangle$ or $\langle a\mid a^6=e \rangle$

compare nuances...

Other: the $Out\pi_1(F)$ of any surface. Btw this is the famous mapping class group of the surface $\cal{MCG}(F)$\cal{MCG}(F)$. To get a real modern grasp on the subjet you should include topological techniques: homotopy, cohomotopy, homology and cohomology, K-theory... you might enter in contact with a types of structures like free groups, free products, amalgamated products, HNN extensions of groups, Grothendieck groups and the like... 2 added study presentations, zum beispiel:$\langle a,b\mid a^2=b^3=e, ab=b^2a \rangle$vs$\langle a,b\mid a^2=b^3=e, ab=ba \rangle$or$\langle a\mid a^6=e \rangle$compare nuances... Other: the$Out\pi_1(F)$of any surface. Btw this is the famous mapping class group of the surface$\cal{MCG}(F)$1 [made Community Wiki] study presentations, zum beispiel:$\langle a,b\mid a^2=b^3=e, ab=b^2a \rangle$vs$\langle a,b\mid a^2=b^3=e, ab=ba \rangle$or$\langle a\mid a^6=e \rangle\$

compare nuances...