  The objective of this work is twofold. On one hand, it is intended as a short
introduction to spin networks and invariants of 3-manifolds. It covers the main
areas needed to have a first understanding of the topics involved in the
development of spin networks, which are described in a detailed but not
exhaustive manner and in order of their conceptual development such that the
reader is able to use this work as a first reading. A motivation due to R.
Penrose for considering spin networks as a way of constructing a 3-D Euclidean
space is presented, as well as their relation to Ponzano-Regge theory.
Furthermore, the basic mathematical framework for the algebraic description of
spin networks via quantum groups is described and the notion of a spherical
category and its correspondence to the diagrammatic representation given by the
Temperley-Lieb recoupling theory are presented. In order to give an example of
topological invariants and their relation to TQFT the construction of the
Turaev-Viro invariant is depicted and related to the Kauffman-Lins invariant.
On the other hand, some results aiming at a decomposition theorem for
non-planar spin networks are presented. For this, Moussouris' algorithm and
some basic concepts of topological graph theory are explained and used,
especially Kuratowski's theorem and the Rotation Scheme theorem.
