Despite the seemingly abstract nature of the subject, higher categories
have seen various applications in other mathematical areas as well as
mathematical physics. We will start off with the definition of
categories and introduce multicategories as their natural
generalization. We will see that algebraic structures such as monoids,
Lie algebras and even categories themselves can be redefined by using
the language of multicategories. Furtheremore, these structures even
permit us to enrich categories over another category. At the end of the
talk I will show how higher categories can be defined in this way.