Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity

We present a pedagogical introduction to SU(2) recoupling theory, focusing on those aspects of the topic which are useful for practical calculations in loop quantum gravity. In particular, we give a self-contained presentation of the powerful graphical formalism, which is an indispensable tool for performing computations in the spin network basis of loop quantum gravity. The use of the graphical techniques in loop quantum gravity is illustrated by several detailed example calculations. Plenty of exercises are included for the benefit of the ambitious student.