Analysis on real and complex manifolds Chapter 1 presents theorems on differentiable functions often used in differential topology such as the implicit function theorem Sards theorem and Whitneys approximation theorem. The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius the lemmata of Poincaré and Grothendieck with applications of Grothendiecks lemma to complex analysis the imbedding theorem of Whitney and Thoms transversality theorem. Chapter 3 includes characterizations of linear differentiable operators due to Peetre and Hormander. The inequalit