1. Preliminaries 2. Construction of $\tilde {E}(G, X)$ 3. Consequences of the slice theorem 4. Topologies on some spaces of maps 5. The covering isotopy property 6. Proof of the covering isotopy theorem 7. Classification of coning data 8. A concordance theorem 9. Existence of coning data 10. Stratified spaces and bundles 11. Extension theory for stratified bundles