The book contains the worked out lecture notes of the courses delivere d at the summer school in Les Houches. They address graduate students and are of interest for researchers as well. The book can be used as a n introduction into three closely related fields: anyons and fractiona l statistics, fractional quantum Hall effect and knot theory. The theo retical papers are occasionally completed by reports on experimental t echniques, and besides of physics some application to biological syste ms can be found.