To be published online at http://www.sf2a.asso.fr/Astrocladistics, a methodology borrowed from biology, is an objective way of understanding galaxy diversity through evolutionary relationships. It is based on the evolution of all the available parameters describing galaxies and thus integrates the complexity of these objects. Through the formalization of the concepts around galaxy formation and evolution, and the identification of the processes of diversification (build up, secular evolution, interaction, merging/accretion, sweeping/ejection), galaxy diversity can be expected to organize itself in a hierarchy. About 500 galaxies described by about 40 observables have now been analysed and several robust trees found. For instance, we show th...