-----------------------------------------------------

  page 4   last line: ... neither elliptic nor hyperbolic
                                               ^^^^^^^^^^
  page 12  equation (4): d theta, not dt

  page 12, 4 lines from bottom: ||b|| <=  ||b||_infinity
           (not the other way around).
  page 31  line 6 (just after displayed equation). 
           The limit statement should refer to: 
                f_r composed with phi,
                ^^^ ^^^^^^^^ ^^^^ ^^^
           not just to f_r. 

  page 34  Problem 7, part (a), second line: if and only if 
           \nu(f_n)
                                                         
  page 35  four lines from bottom:  "Hunziger", not "Huniziger"

  page 40, second line of large display: f_n'(\phi(z))
           not f_n(\phi(z))  (the derivative symbol is missing)

  page 48  last line: \Psi_{\alpha,0,b}(\Pi) instead of 
                      \psi_{\alpha,0,b}(\pi)

                   (Capital \psi and \pi instead of lower-case)

  page 55  eight lines from the bottom: delete the second 
           hyphen in "Julia-Carathe'odory".

  page 57  last line of statement of Julia-Carath. Theorem:
           ``.. omegabar eta.." not "omega etabar"
  page 67  second line: "w_0 \in \Pi" (not "\omega_0 \in \Pi").
                                             ^^^^^
           four lines from bottom: "p \in \Pi" 
           (not \phi \in \Pi).                                                     
                 ^^^

  page 71  in statement of Corollary: 
                phi is a univalent self-map  of U
                         ^^^^^^^^^
           (not just a holomorphic one: the Cor. is false for        
           arbitrary self-maps, as I go to great lengths to 
           show in Chapter 10.)

  page 74  Exercise 12: 
               in second line: "boundary of U" not just "U"
 
               in third line:   sup_n|\phi_n'(\zeta)|  
               (subscript "n" is missing)


  page 98, Displayed statement in next-to-last paragraph:  
           "If phi is a univalent self-map ..."
               ^^^

  page 103, Exercise 12, part (a):
            Show that if T is compact, 
                      ^^^^^^^^^^^^^^^
            then the diagonal entries of the matrix are the 
            only eigenvalues of T.

      (The Backward Shift on H^2 is a counterexample to the
       result of part (a) as it is stated.)

  page 110 two lines after first display: The word "define" 
           occurs twice.  Delete one! 

  page 196  Middle of page, two lines below displayed formula:
      " ... u=|f|^2 ..."  not "... u = |f'|^2 .."

  page 178  second line before the Littlewood-Paley Identity:
      "... it is more convenient to put a little more care ..."
                                 ^^

  page 189  next-to-last line of large display:

            Instead of   ||z||^2 
 
            there should appear

                         ||\phi||^2 - |\phi(0)|^2


            which results from the integral of N_\phi that 
            occurs in the line above upon appplying the 
            change-of-variable formula (4) on p 179 
            to the function f(z) = z.

  page 190  right-hand side of inequality (22): 
            Integrate with respect to dA(z), not dA(w). 
                                ^^^^^

  page 200  third line before last paragraph:"Mascioni", not 
           "Maschioni".

  page 208  references [KrM '90] and [KrM '92]: "Kriete", not" 
            Kreite".(same error on index entry, page 218)


  page 211  reference [STa '72]  IUMJ 23 (1973)  
                                      ^^
            (vol. 23, not vol. 125)

  page 212  reference [Sk1 '87] Composition semigroups 
                                            ^^^^^^^^^^
                          (not  Composition operators)
                                            ^^^^^^^^^
****************
In addition, I've been informed of these errors that I haven't 
checked yet:

  page 49  fourth line from top: y = Ax + Bx^\gamma

                            (not y = A + Bx^\gamma)

  page 139  In the estimates involving w_{n+1} - w_n, one 
            should not take the
            specific constants claimed there too seriously!

****************
I'd like to thank Mihaela Poplicher, Maria Tjani, John Clifford, Aristomenis
Siskakis,  P. Galanopoulos, and Raymond Mortini for their help here.

The latest corrections are available by anonymous ftp from:
          math.msu.edu 
in the file:
          pub/papers/shapiro

Please let me know about any other mistakes you might encounter.

... Joel Shapiro  (shapiro@math.msu.edu)