This graduate-level textbook includes features of research monographs and surveys of recent research on the analysis and geometry of differential equations in the real and complex domain. It covers normal forms and desingularization, including analytic differential equations in the complex domain, holomorphic foliations and their singularities, finitely generated groups of conformal germs, and desingularlization in the plane; singular points of planar analytic vector fields, including planar vector fields with characteristic trajectories, holonomy and first integrals, and complex separatrices of holomorphic foliations; the local and global theory of linear systems, including Riemann-Hilbert problems; functional moduli of analytic classifications of resonant germs and their applications, including complex saddles and saddle-nodes; and global properties of complex polynomial foliations. The authors provide a crash course on functions of several complex variables and elements of the theory of Riemann spaces. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)