In this work we present an introduction of Groups Theory with emphasis on group
homomorphism. Our main goal is to enunciate and demonstrate the Homomorphism
Theorem. This theorem gives us a characterization of the quotient group of the do-
main of a homomorphism by its nucleus and an explicit way of obtaining from a ho-
momorphism a quotient group. For this, we do a whole study on group isomorphism.
This study becomes relevant, due to the advantages of knowing isomorphic groups.
We say that isomorphic groups behave, in their algebraic structure, in the same
way. So there is no distinction when it comes to its operations, properties, that is,
the elements operate in the same way. Besides this theorem, we will bring other
important results for group theory, as for example: the Cayley Theorem and the
Lagrange Theorem.
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