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In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. Viewed infinitesimally, a connection is a way of differentiating geometric data in such a manner that the derivative is also geometrically meaningful.

Guide to connections

• For connections as they are normally first encountered in tensor analysis, see covariant derivative.
• For connections as they are first encountered in differential geometry, see affine connection, connection (vector bundle), and connection (principal bundle).
• For connections using differential forms, see connection form, Cartan connection, and Ehresmann connection.
• For connections as they are frequently used in gauge theory and physics, see gauge covariant derivative and gauge connection.