Mini-course: property of rapid decay

These are the notes for the mini-course on the property of rapid decay given at the Erwin Schr\"odinger Institute in Vienna between March 14th and 18th, 2016, as a part of the Measured Group Theory program. They include parts which were omitted during the lectures, and omit some parts which were included in the lectures (and now I think that they shouldn't have been). We explore the definitions of property RD and its permanence properties, discuss the centroid property and relative centroid property defined by Mark Sapir, and give proofs that certain classes of groups have RD.