Family of Finite Blaschke Products in $$C^*$$-Algebras

In the paper, a new class of universal $$C^*$$ -algebras, namely, Blaschke $$C^*$$ -algebras, are constructed, for which the relations between generators are defined by a family of finite Blaschke products. Two approaches to constructing a universal object are proposed, one of which is related to the inductive limit of Toeplitz algebras, and the other to an isometric representation of the uniform Blaschke algebra. $$C^*$$ -algebras generated by isometric representations of a Blaschke algebra in the algebra of bounded linear operators on generalized Hardy spaces with a probability measure and, in particular, with a Haar measure are considered in detail.