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A 4-manifold is a topological manifold locally modeled on ${\mathbb{R}}^4$, with a half-space model if a boundary is allowed. Examples include the four-sphere, the Complex projective plane and the product of two spheres $S^2\times S^2$. Its middle-dimensional intersection form pairs degree-two homology classes. Dimension four is special because an embedded two-dimensional surface has the same dimension as its complementary normal directions; intersections and their removal become particularly subtle. A smooth four-manifold carries additional differentiable structure, which is not determined merely by its local topological model.