This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ- ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it- self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin- ciple, Ergodic theory), while the ones inside representation theory...