Finitely dominated compacta need not have finite type.- Fixed points in finitely dominated compacta: the geometric meaning of a conjecture of H. Bass.- Splitting homotopy idempotents.- Approximate fibrations-a geometric perspective.- Local n-connectivity of quotient spaces and one-point compactifications.- A simple-homotopy approach to the finiteness obstruction.- Generalized three-manifolds.- Some properties of deformation dimension.- Dimension, cohomological dimension, and cell-like mappings.- Embedding compacta up to shape.- On shape concordances.- Complement theorems in shape theory.- Embeddings in shape theory.- Under what conditions are shape homology and steenrod homology isomorphic ?.- Strong shape theory.- Inverse limits and resolutions.- Application of the shape theory in the characterization of exact homology theories and the strong shape homotopic theory.