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