  This final degree project is devoted to study the topological classification
of complex plane curves. These are subsets of $\mathbb{C}^2$ that can be
described by an equation $f(x,y)=0$. Loosely speaking, curves are said to be
equivalent in a topological sense whenever they are ambient homeomorphic, i.e.,
there exists an orientation-preserving homeomorphism of the ambient space
carrying one curve to the other. The project's aim is to develop operative and
clear conditions to determine whether two curves are equivalent. Curves will be
shown to be decomposable into branches: sets that can be explicitly
parametrised in the form $x=\phi(t), y=\psi(t)$. These parametric expressions
will be analysed to extract a complete numerical invariant for the
classification of branches: the Puiseux characteristic. The intermediate key
result to lend this notion with topological weight is that a branch can be
completely described through its associated knot, arising from the intersection
of the branch with a small enough 3-sphere. The combination of these
above-mentioned facts will then culminate in the project's most powerful
result, which assures that two curves are equivalent if and only if their
branches share the same Puiseux characteristics and intersection numbers.
