Etiquetamiento gracioso de árboles

The Graceful Tree Conjecture was published almost 40 years ago and nowadays it is still an open problem. It seems as difficult to solve as it is to enunciate: every tree admits a vertex labeling on 0, 1, ..., n-1 such that the set of values of the differences of the numbers assigned to the ends of each edge is the set {1, 2, ..., n-1}. This Thesis has two major parts. The first one is a review of the most remarkable advances towards the solution of the problem. The second one is a self-developed method to gracefully label trees using adjacency matrices