- Introduction to the Notes of the School on Analysis and Geometry in Metric Spaces. - Geometric Inequalities on Riemannian and Sub-Riemannian Manifolds by Heat Semigroups Techniques. - Differentiation of Measures in Metric Spaces. - Sobolev Spaces in Extended Metric-Measure Spaces. - Brief Survey on Functions of Bounded Variation (BV) in Metric Setting.