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SECTION 1 INTRODUCTION SECTION 2 DEFORMATION THEORY OF LIE ALGEBRAS SECTION 3 VESSIOT STRUCTURE EUATIONS SECTION 4 LINEAR AND NONLINEAR JANET SEQUENCES SECTION 5 DEFORMATION THEORY OF LIE EQUATIO?NS SECTION 6 EXPLICIT COMPUTATIONS SECTION 7 CONCLUSION SECTION 8 BIBLIOGRAPHY APPENDIX 1 ABSTRACT SECTION 1 INTRODUCTION SECTION 2 HOMOLOGICAL ALGEBRA SECTION 3 DIFFERENTIAL SYSTEMS SECTION 4 DIFFERENTIAL MODULES SECTION 5 APPLICATIONS A) Riemann tensor B) Weyl tensor C) Parametrization SECTION 6 CONCLUSION REFERENCES FOR THE APPENDIX 1 APPENDIX 2 SECTION 1.1 WEYL TENSOR 1.2 Dimension 3 1.3 Dimension 4 1.4 Dimension 5 REFERENCES FOR THE APPENDIX 2 APPENDIX 3 ABSTRACT SECTION 1 FIELD/MATTER COUPLINGS REFERENCES FOR THE APPENDIX 3 ±à¼­ÊÖ¼Ç