The analysis of distributional data (probability density functions or histogram data) has recently gained increasing attention in the applications. Distributional data are often observed by themselves, or as result of aggregation of large streams of data. The course will provide an introduction to the analysis of these data using a Functional Data Analysis (FDA) approach, grounded on the perspective of Bayes spaces. These spaces are mathematical spaces whose points are densities (or, more generally, measures), which generalize to the FDA setting the Aitchison simplex for multivariate compositional data. The course will give an overview of the theory of Bayes spaces, as well as of statistical methods developed in this setting. All the methods will be illustrated through examples from real case studies.