This volume of the Encyclopaedia contains two contributions: the first one, "Harmonic Analysis on Homogeneous Spaces", is written by V.F.Molchanov, the second one, "Representations of Lie Groups and Special Functions", by N.Ya. Vilenkin and A.U. Klimyk. Molchanov focuses on harmonic analysis on semi-simple spaces, whereas Vilenkin and Klimyk treat group theoretical methods also with respect to special functions, orthogonal polynomials and integral transforms. Both contributions are surveys introducing readers to the above topics and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.