Eigenvalues Embeddings and Generalised Trigonometric Functions The main theme of the book is the study from the standpoint of s numbers of integral operators of Hardy type and related Sobolev embeddings. In the theory of s numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p Laplacian 1 Basic material 2 Trigonometric generalisations 3 The Laplacian and some natural variants 4 Hardy operators 5 s Numbers and generalised trigonometric functions 6 Estimates of s numbers of weighted Hardy operators 7 More refined estimates 8 A non linear integral system 9 Hardy operators on variable exponent spaces