Back to basics: Another look at Morita equivalence

One of the basic forms of Morita equivalence is the following: If p is a projection in a *-algebra A, then the subalgebra pAp is Morita equivalent to the ideal ApA. We shall study various examples of this, we will need both the Fell and the Rieffel version of Morita equivalence, pass through old subjects like spherical functions and hermittian *-algebras. We will end with seeing how this perspective gives insight in the Hecke algebras of Bost-Connes and the C*-algebras of integral domains studied by Cuntz-Li.