Lie groups provide a formalization of the concept of symmetry in the classical theory of special functions, combinatorics, and physics. From this viewpoint, DAHA describes abstract Fourier transforms, especially those making the Gaussian Fourier-invariant. The classical Fourier transform, the Hankel transform, and the one from the theory of Gaussian sums are well known examples. Thus DAHA formalizes an important part of the classical Fourier analysis. The Verlinde algebras are the key finite-dimensional examples. There exist three different Verlinde algebras of type A 1: 1) the one connected with the Hankel transform, and, hopefully, with the massless conformal field theory, 2) the major Verlinde algebra associated with the Kac-Moody fusion and the massive CFT and, 3) the algebra presumably describing the fusion of the (1,p)-Virasoro model. They will be discussed in the lectures.