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Geometric numerical integration is concerned with deriving numerical schemes for differential equations preserving geometric properties of differential equations at a discrete level. In this lecture I will given an introduction to geometric numerical integration and how it relates to standard numerical integration of differential equations. I will provide a short review of the classical notions of errors in numerical schemes and present specific examples from differential equations arising in various areas of the mathematical sciences illustrating that these notions may be inconclusive to assess the practical usability of numerical schemes for these real-world problems. I will then discuss how geometric numerical integrators could remedy the arising issues. Specific attention will be paid to Hamiltonian structures and conservation laws.