The aim of this mini-course is to provide a partial survey of the theory and practice of statistical methods with functional data [often referred to as Functional Data Analysis (FDA)].

Among the different topics of interest in this field I will try to consider the following ones:

• Introduction and motivation. A real-data example.
• How to handle in practice the functional data.
• Some basic hints on the underlying probability theory: functional probability models, functional expectation, the Law of Large Numbers and the Central Limit Theorem in function spaces.
• The notions of median and mode in FDA.
• Depth measures for functional data.
• The Random Projections (RP) method. RP-based depth measures.
• The linear regression model with functional regressor and a scalar response.
• An introduction to classification with functional data.
  
  

No previous background on FDA is assumed. The style will be expository: the proofs as well as many technicalities will be omitted. However, the focus will be on mathematical aspects (rather than on computational problems or specific applications). The goal is discussing topics with a rich mathematical structure (quite different to that of their finite-dimensional counterparts) where many interesting problems remain open.