The textbook "Rasshheplyaemye DAU v chastnyh proizvodnyh" offers a comprehensive analysis of systems of differential equations in partial derivatives. It is assumed that the matrices preceding the sought vector functions are degenerate throughout the entire domain of definition. The work defines the index for differential-algebraic equations (DAU) in partial derivatives and proves existence and uniqueness theorems for linear DAUs with constant and variable coefficients, as well as for quasi-linear DAUs. Additionally, the concept of decomposable systems is introduced, and the structure of their solutions is examined. This book is aimed at professionals and students engaged in the theory and application of differential equations in mathematics and engineering.