What are the parts of bullfighting?

Answer 1

A large heavy rose colored cape - a capote
A smaller, lighter cape - the muleta
A sword - estoque
In addition, banderillas (decorated barbed sticks) and the picador's lance.
These are the main pieces of 'equipment' used in a bullfight.

Answer 2

Matadors use a special sword called estoque or espada to kill the bull. It has a slightly curved blade to facilitate its entry onto the bull and to magnify the damage it causes.