Authors’ summary: We study the \(C^{*}\)-algebra generated by Toeplitz operators with piecewise continuous symbols acting on the Bergman space \({\mathcal{A}}^2({\mathbb{D}})\) on the unit disk \({\mathbb{D}}\) in \({\mathbb{C}}\). We describe explicitly each operator from this algebra and characterize Toeplitz operators which belong to the algebra.