Taft  algebras are finite dimensional algebras distantly related to the CCR-algebra. They admit a Hopf algebra structure and they were introduced by Taft in order to show that the antipode of a finite dimensional Hopf algebra can be of an arbitrary (even) order. Remarkably every Taft Hopf algebra admits infinitely many coideal subalgebras, which is in contrast with the case of group algebras associated with finite groups and Hopf algebras of functions on finite groups (in the latter two cases they correspond to subgroups of a given group). In my talk I will

    -  describe coideals of Taft Hopf algebras;

    - explain the concept of (co)integrals on coideal subalgebras of a Hopf algebra and describe them in case of the Taft Hopf algebra;

    - give a sketch of the theory of (co)integrals on coideal subalgebras of general Hopf algebras.

Partially based on joint work with A. Chirvasitu and P. Szulim.