Class-notes and references for APM 581 and APM 582 Textbooks: A. Spivak, A Comprehensive Introduction to Differential Geometry, vol I. 3rd ed., 1999, Publish or Perish. A. Spivak, A Comprehensive Introduction to Differential Geometry, vol II. 3rd ed., 1999, Publish or Perish. Class-notes APM 581 fall 2010 class notes APM 582 spring 2011 class notes old class notes (APM 581 spring 2009) Selected other texts for differential geometry MIT open courseware (Lie Groups) W. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd ed. (2002). R. Abraham, J. Marsden, and T. Ratiu, Manifolds, Tensor Analysis, and Applications Applied Mathematical Sciences v. 75, (1988) Springer. S. Sternberg, Lectures on Differential Geometry, (1999) AMS Chelsea Publishing Selected other texts for control and geometry of dynamical systems A. Isidori, Nonlinear Control Systems, (1995) Springer. H. Nijmeier and A. van der Schaft, Nonlinear Dynamical Control Systems, Springer. A. Agrachev Snd Y. Sachkov Control theory from the geometric viewpoint, Springer. V. Jurdjevic, Geometric control theory , (2000), Cambridge UP. A. Bloch, P. Crouch, J. Baillieul, and J. Marsden, Nonholonomic echanics and Control, (2003) Springer. F. Bullo and A. Lewis, Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems, (2004), Springer. Last updated: January 13, 2011