本书是在1996年出版的《常微分方程》（德文）一书的基础上编写而成的，书中主要介绍常微分方程的基础理论。内容包括：可积一阶微分方程，微分方程解的存在性和唯一性，微分方程的初极值问题，边值问题和特征值问题，稳定性与渐进稳定性理论。阅读本书需要具备一定的计算代数、线性代数及泛函分析的基础知识。适用于高校数学专业、牧业专业和计算机科学等相关专业的本科生和研究生。 PrefaceNotetotheReaderIntroductionChapterI.FirstOrderEquations:SomeIntegrableCases1.ExplicitFirstOrderEquations2.TheLinearDifferentialEquation.RelatedEquationsSupplement:TheGeneralizedLogisticEquation3.Dif　ferentialEquationsforFamiliesofCurves.ExactEquations4.ImplicitFirstOrderDifferentialEquationsChapterII:TheoryofFirstOrderDifferentialEquations5.ToolsfromFunctionalAnalysis6.AnExistenceandUniquenessTheoremSupplement:SingularInitialValueProblems7.ThePeanoExistenceTheoremSupplement:MethodsofFunctionalAnalysis8.ComplexDifferentialEquations.PowerSeriesExpansions9.UpperandLowerSolutions.MaximalandMinimalIntegralsSupplement:TheSeparatrixChapterIII:FirstOrderSystems.EquationsofHigherOrder10.TheInitialValueProblemforaSystemofFirstOrderSupplementI:DifferentialInequalitiesandInvarianeSupplementII:DifferentialEquationsintheSenseofaratheodory11.InitialValueProblemsforEquationsofHigherOrderSupplement:SecondOrderDifferentialInequalities12.ContinuousDependenceofSolutionsSupplement:GeneralUniquenessandDependenceTheorems13.DependenceofSolutionsonInitialValuesandParametersChapterIV:LinearDifferentialEquations14.LinearSystems15.HomogeneousLinearSystems16.InhomogeneousSystemsSupplement:L1-EstimationofC-Solutions17.SystemswithConstantCoefficients18.MatrixFunctions.InhomogeneousSystemsSupplement:FloquetTheory19.LinearDifferentialEquationsofOrdern20.LinearEquationsofOrdernwithConstantCoefficientsSupplement:LinearDifferentialEquationswith　PeriodicCoefficientsChapterV:ComplexLinearSystems21.HomogeneousLinearSystemsintheRegularCase22.IsolatedSingularities23.WeaklySingularPoints.EquationsofFuchsianType24.SeriesExpansionofSolutions25.SecondOrderLinearEquationsChapterVI:BoundaryValueandEigenvalueProblems26.BoundaryValueProblemsSupplementI:Maximuma