This volume contains a systematic presentation of the general theory of differential equations on complex manifolds. The six chapters deal with questions concerning qualitative (asymptotic) theory of partial differential equations as well as questions about the existence of solutions in spaces of ramifying functions. Attention is given to applications, and particular problems connected with the continuation of (real) solutions to differential equations and with mathematical theory of diffraction are solved here. The book is self-contained, and includes up-to-date results. All necessary terminology is explained. The text should be of use to graduate students and researchers interested in differential equations in partial derivatives, complex analysis, symplectic and contact geometry, integral transformations and operational calculus, and mathematical physics.