Phylogenetic approaches to classification have been heavily developed in biology by bioinformaticians. But these techniques have applications in other fields, in particular in linguistics. Their main characteristics is to search for relationships between the objects or species in study, instead of grouping them by similarity. They are thus rather well suited for any kind of evolutionary objects. For nearly fifteen years, astrocladistics has explored the use of Maximum Parsimony (or cladistics) for astronomical objects like galaxies or globular clusters. In this lesson we will learn how it works. 1 Why phylogenetic tools in astrophysics? 1.1 History of classification The need for classifying living organisms is very ancient, and the first classification system can be dated back to the Greeks. The goal was very practical since it was intended to distinguish between eatable and toxic aliments, or kind and dangerous animals. Simple resemblance was used and has been used for centuries. Basically, until the XVIIIth century, every naturalist chose his own criterion to build a classification. At the end, hundreds of classifications were available, most often incompatible to each other. The criteria for this traditional way of classifying is the subjective appearance of the living organisms. During the XVIIIth a revolution occurred. Scientists like Adanson and Linné devised new ways of classifying the objects and naming the classes. Adanson realised that all the observable traits should be used, giving birth to the mul-tivariate clustering and classification activity (Adanson, 1763). Linné based his binomial nomenclature on neutral names unrelated whatsoever to any property of the classes. We can realise the success of these two ideas more than two centuries and a half later!