The Racah algebra is a very rich algebra appearing in more than one field of mathematical physics: Superintegrable Hamiltonian systems on the hypersphere, multivariate Racah Polynomials, and su(1,1) recoupling problem. In this presentation, we will use the latter to construct the algebras of rank 0, 1, and 2. For the (trivial) rank-0 case, it leads to the well-known Clebsch-Gordan coefficients. The representation of the rank-1 case is known, but very little is known about higher-rank cases. We will then explore many properties of the Racah algebra and discuss rank-2 representations. (This is a joint work with Prof. Sarah Post.)