Lecture 1: Transversally elliptic operators.- Lecture 2: The index of transversally elliptic operators.- Lecture 3: The excision and multiplicative properties.- Lecture 4: The naturality of the index and the localization theorem.- Lecture 5: The index homomorphism for G = S1.- Lecture 6: The operators for G = S1.- Lecture 7: Toral actions with finite isotropy groups.- Lecture 8: The index homomorphism for G = Tn.- Lecture 9: The cohomology formula.- Lecture 10: Applications.