Theta Criteria are based on operator's theory and matrices decompositions. The main idea is to evaluate differences between sets of operators' eigenvalues & eigenvectors or eigenfunctions. Theta Criteria will lead to more efficient analysis, optimization and prognosis of multivariate systems and applications. Theta Criteria can be used for data set mining and image processing. The book is designed as a complementary tool for applied mathematics methods. More information at: www.ThetaCriteria.com Keywords: Block matrices, Canonical analysis, Condition, Determinant, Eigenfunctions, Eigenpair, Eigenvalues, Eigenvectors, Euclidean norm, Financial Problems Analysis, Finite linear vector space, Formal linear algebra methods, Hilbert theorem, IED Identification, Ill-defined matrices, Matrices Closeness Criteria, Matrices with variable block linkages, Matrix condition, Matrix determinant, Matrix block linkage, Matrix norm, Matrix rank, Matrix trace, Medical Applications, Multiple Regression, Multivariate data processing, Norm, Ordered eigenvalues set, Orthonormalized basis, Orthonormalized eigenvectors set, Pair of eigenpairs, Positively defined matrix, Principle Components Analysis, Real numbers field, Sequence cardinality, Spectral theorem, Symmetrical positively defined matrices sequence, Theta Criteria, Theta Criteria Preliminary Conditions, Theta Criteria properties, Weighted eigenvector