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The aim of this book is to define and study the $({cal{T}}_{!a}, {cal{T}}_{!b})$-pseudosymmetric, $({cal{T}}_{!a}, {cal{T}}_{!b},S^{ell})$-pseudosymmetric, $({cal{T}}_{!a},S_{{cal{T}}_{b}})$-pseudosymmetric and $({cal{T}}_{!a},S_{{cal{T}}_{!b}},S^{ell})$-pseudosymmetric semi-Riemannian manifolds. Then study these type of pseudosymmetry for $(N(K),xi)$-semi-Riemannian manifolds.