Algorithms of Estimation for Nonlinear Systems : A Differential and Algebraic Viewpoint This book acquaints readers with recent developments in dynamical systems theory and its applications with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems in particular so called input affine or bilinear systems which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools including differential algebraic theory observer design for nonlinear systems and generalized canonical forms. Preface Analysis of input affine nonlinear processes Basic Definitions of Differential Algebras Algebraic Observability Condition for Nonlinear systems and External behaviour Generalized Observability Canonical Forms Observer Synthesis Tracking and Stabilization Problems Parametric and State Estimation Observer synthesis for a more general class of Nonlinear Systems A Separation Principle for Nonlinear Systems Some uncommon observers with interesting applications Appendix A Singularity Treatment Appendix B Some properties for Nonlinear Systems.