Main research/educational fields of this area are Theory of differential equations and Analysis on manifolds, which are both fundamental research fields in the Analysis. By using many tools as Complex analysis, Algebraic analysis, Functional analysis, Algebraic geometry, Topology, Generalized functions, we will study Theory of complex functions in one or several variables, Differential equations in real or complex domains, Complex manifolds and Algebraic manifolds. In particular, on local or microlocal theory of linear differential equations, Algebraic analysis of pseudo-differential operators, Singularity of PDE in the complex domain or Algebraic geometry, starting from systematic study, we aim for the latest frontiers of subjects.