Because of its new results and techniques and its comprehensive coverage of the classification of homotopy types of simply-connected complexes with cells in only four consecutive dimensions and dual case, the book is necessary reading for graduate students and researchers in the field and for others who may wish to use results on homotopy classification in other areas such as classification of manifolds.

• Introduction ; 1. Linear extension and Moore spaces ; 2. Invariants of homotopy types ; 3. On the classification of homotopy types ; 4. The CW-tower of categories ; 5. Spaniert-Whitehead duality and the stable CW-tower ; 6. Eilenberg-Mac Lane functors ; 7. Moore functors ; 8. The homotopy category of (n -1)-connected (n+1)-types ; 8. On the homotopy classification of (n-1)-connected (n+3)-dimensional polyhedra, n>4 ; 9. On the homotopy classification of 2-connected 6-dimensional polyhedra ; 10. Decomposition of homotopy types ; 11. Homotopy groups in dimension 4 ; 12. On the homotopy classification of simply connected 5-dimensional polyhedra ; 13. Primary homotopy operations and homotopy groups of mapping cones ; Bibliography ; Index