This Paper Contributes to the Theoretical Analysis of Linear Differential Algebraic Equations of Higher Order As Well As of the Regularity and Singularity of Ma¬Trix Polynomials. some Invariants and Condensed Forms Under Appropriate Equivalent Transformations Are Given For Systems of Linear Higher-Order Differential-Algebraic Equations’ With Constant and Variable Coefficients. Inductively, Based on Condensed Forms the Original Differential-Algebraic Equations System Can Be Transformed By Differentiation-And-Elimination Steps into an Equivalent Strangeness-Free System, from Which the Solution Behaviour (Including Consistency of Initial Conditions and Unique Solvability) of the Original Differential-Algebraic Equations System and Related Initial Value Problem Can Be Directly Read Off.