The chapter introduces the topology of four-dimensional manifolds, focusing on the classification of 1-connected 4-manifolds and topological end recognition. The main impact of the discovery of a homotopy theoretic criterion for embedding a topological 2-handle in a smooth 4-manifold with boundary is outlined. This criterion, developed by Andrew Casson, allows for the classification of 1-connected 4-manifolds and has applications to nonsimply connected problems such as knot concordance. The author describes the stages of the discovery, from Casson's theory of "flexible handles" to the systematic exploitation of geometric control over Casson handles. The chapter also presents key theorems and corollaries, including the classification of almost-smooth 4-manifolds and the existence of non-homeomorphic but homotopy equivalent 4-manifolds. The proofs are detailed, with specific examples and diagrams provided to illustrate the concepts.The chapter introduces the topology of four-dimensional manifolds, focusing on the classification of 1-connected 4-manifolds and topological end recognition. The main impact of the discovery of a homotopy theoretic criterion for embedding a topological 2-handle in a smooth 4-manifold with boundary is outlined. This criterion, developed by Andrew Casson, allows for the classification of 1-connected 4-manifolds and has applications to nonsimply connected problems such as knot concordance. The author describes the stages of the discovery, from Casson's theory of "flexible handles" to the systematic exploitation of geometric control over Casson handles. The chapter also presents key theorems and corollaries, including the classification of almost-smooth 4-manifolds and the existence of non-homeomorphic but homotopy equivalent 4-manifolds. The proofs are detailed, with specific examples and diagrams provided to illustrate the concepts.