I. Error computations à la Gauss.- 1. The different approaches.- 2. Finite dimensional examples.- 3. An intuitive introduction to error structures.- 4. Weakly and strongly random errors.- II. Probabilistic and Functional Models.- 5. Strongly continuous semi-groups and Dirichlet forms.- 6. Error structures.- 7. Images and products of error structures.- 8. The gradient and the sharp and other calculation tools.- 9. Error structures on fundamental spaces.- III. The subtleness of the notion of bias.- 10. Approximation and bias operators.- 11. Computations and simulation methods.- IV. Error structures and its applications.- 12. Statistical identification of error structures.- 13. The instantaneous structure of a stochastic process.- 14. Models inspired by finance.- 15. Examples in Physics.- 16. The principle of arbitrary functions and error structures.- V. Historical elements and research themes.- 17. Error calculations from Gauss and Laplace.- 18. Extensions and open questions.- Hints forexercises.- Pedagogical References.- Chronological Bibliography.