Illustrated guide to perverse sheaves I

This will be a mini-course (consisting of six or seven lectures) intended to give an informal introduction to perverse sheaves. Perverse sheaves are usually treated rather formally. I will try to give a more geometric introduction with lots of pictures, discussing in detail examples on curves and surfaces. I will also discuss nearby and vanishing cycles, characteristic cycles and some Hodge theoretic aspects. I will also discuss the decomposition theorem (with examples) as well as de Cataldo and Migliorini's Hodge theoretic proof.