This chapter is from the book "Equations Différentielles à Points Singuliers Réguliers" by Pierre Deligne, published by Springer-Verlag in 1970. The book is part of the Lecture Notes in Mathematics series and is edited by A. Dold and B. Eckmann. It covers the following topics: 1. **Introduction** 2. **Dictionnaire** - Systems of local equations and fundamental groups - Integrable connections and systems of local equations - Translation into terms of first-order partial differential equations - Differential equations of the \(n\)-th order - Differential equations of the second order - Finite-determined multiform functions 3. **Regular Connections** - Regularity in dimension one - Growth conditions - Logarithmic poles - Regularity in dimension \(n\) - Existence theorem - Comparison theorem - Regularity theorem 4. **Applications** - Nilsson functions - Monodromy theorem, following Brieskorn The book provides a comprehensive treatment of regular singular point differential equations, including theoretical foundations and applications.This chapter is from the book "Equations Différentielles à Points Singuliers Réguliers" by Pierre Deligne, published by Springer-Verlag in 1970. The book is part of the Lecture Notes in Mathematics series and is edited by A. Dold and B. Eckmann. It covers the following topics: 1. **Introduction** 2. **Dictionnaire** - Systems of local equations and fundamental groups - Integrable connections and systems of local equations - Translation into terms of first-order partial differential equations - Differential equations of the \(n\)-th order - Differential equations of the second order - Finite-determined multiform functions 3. **Regular Connections** - Regularity in dimension one - Growth conditions - Logarithmic poles - Regularity in dimension \(n\) - Existence theorem - Comparison theorem - Regularity theorem 4. **Applications** - Nilsson functions - Monodromy theorem, following Brieskorn The book provides a comprehensive treatment of regular singular point differential equations, including theoretical foundations and applications.