Introduction General results about H.I. spaces Schreier families and repeated averages The space ${X=T [G,(\mathcal{S}_{n_j}, {\tfrac {1}{m_j})}_{j},D]}$ and the auxiliary space ${T_{ad}}$ The basic inequality Special convex combinations in $X$ Rapidly increasing sequences Defining $D$ to obtain a H.I. space ${X_G}$ The predual ${(X_G)_*}$ of ${X_G}$ is also H.I. The structure of the space of operators ${\mathcal L}(X_G)$ Defining $G$ to obtain a nonseparable H.I. space ${X_G^*}$ Complemented embedding of ${\ell^p}, {1\le p < \infty}$, in the duals of H.I. spaces Compact families in $\mathbb{N}$ The space ${X_{G}=T[G,(\mathcal{S}_{\xi_j},{\tfrac {1}{m_j})_{j}},D]}$ for an ${\mathcal{S}_{\xi}}$ bounded set $G$ Quotients of H.I. spaces Bibliography.
