This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall''s diffeomorphisms and h-cobordism, and Rohlin''s theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin''s theorem using spin structures. There is an introduction to Casson handles and Freedman''s work including a chapter of unpublished proofs on exotic R4''s. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.

This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall''s diffeomorphisms and h-cobordism, and Rohlin''s theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin''s theorem using spin structures. There is an introduction to Casson handles and Freedman''s work including a chapter of unpublished proofs on exotic R4''s. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.

This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall''s diffeomorphisms and h-cobordism, and Rohlin''s theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin''s theorem using spin structures. There is an introduction to Casson handles and Freedman''s work including a chapter of unpublished proofs on exotic R4''s. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.