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Finite dimensional modular Lie superalgebras over algebraically closed fieldswith indecomposable Cartan matrices are classified under some technical, mostprobably inessential, hypotheses. If the Cartan matrix is invertible, thecorresponding Lie superalgebra is simple otherwise the quotient of the derivedLie superalgebra modulo center is simple (if its rank is greater than 1).Eleven new exceptional simple modular Lie superalgebras are discovered. Severalfeatures of classic notions, or notions themselves, are clarified orintroduced, e.g., Cartan matrix, several versions of restrictedness incharacteristic 2, Dynkin diagram, Chevalley generators, and even the notion ofLie superalgebra if the characteristic is equal to 2. Interesting phenomena incharacteristic 2: (1) all simple Lie superalgebras with Cartan matrix areobtained from simple Lie algebras with Cartan matrix by declaring several (any)of its Chevalley generators odd; (2) there exist simple Lie superalgebras whoseeven parts are solvable. The Lie superalgebras of fixed points of automorphismscorresponding to the symmetries of Dynkin diagrams are also listed and theirsimple subquotients described.

Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix