  We study theoretically the structure of double pionic atoms, in which two
negatively charged pions ($\pi^-$) are bound in the atomic orbits. The double
pionic atom is considered to be an interesting system from the point of view of
the multi bosonic systems. In addition, it could be possible to deduce valuable
information on the isospin $I = 2$ $\pi\pi$ interaction and the pion-nucleus
strong interaction. In this paper, we take into account the $\pi\pi$ strong and
electromagnetic interactions, and evaluate the effects on the binding energies
by perturbation theory for the double pionic atoms in heavy nuclei. We
investigate several combinations of two pionic states and find that the order
of magnitude of the energy shifts due to the $\pi\pi$ interaction is around 10
keV for the strong interaction and around 100 keV for the electromagnetic
interaction for the ground states.
