Contents -- Preface -- 1. Introduction -- 2. Basic Properties of Multiplier Convergent Series -- 3. Applications of Multiplier Convergent Series -- 4. The Orlicz-Pettis Theorem -- 5. Orlicz-Pettis Theorems for the Strong Topology -- 6. Orlicz-Pettis Theorems for Linear Operators -- 7. The Hahn-Schur Theorem -- 8. Spaces of Multiplier Convergent Series and Multipliers -- 9. The Antosik Interchange Theorem -- 10. Automatic Continuity of Matrix Mappings -- 11. Operator Valued Series and Vector Valued Multipliers -- 12. Orlicz-Pettis Theorems for Operator Valued Series -- 13. Hahn-Schur Theorems for Operator Valued Series -- 14. Automatic Continuity for Operator Valued Matrices -- Appendix A. Topological Vector Spaces -- Appendix B. Scalar Sequence Spaces -- Appendix C. Vector Valued Sequence Spaces -- Appendix D. The Antosik-Mikusinski Matrix Theorems -- Appendix E. Drewnowski's Lemma -- References -- Index.