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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                  SCHEDULE 13D
                                 (Rule 13d-101)

                               (Amendment No. 31)

                         ______________________________

                              TELECOM ITALIA S.P.A.
                                (Name of Issuer)

ORDINARY SHARES OF EURO 0.55 PAR VALUE EACH                 87927W10
     (Title of class of securities)                       (CUSIP number)

                           ALEXANDER ROSENZWEIG, ESQ.
                     VICE PRESIDENT AND CHIEF LEGAL OFFICER
                           PIRELLI NORTH AMERICA, INC.
                              246 STONERIDGE DRIVE
                                    SUITE 400
                         COLUMBIA, SOUTH CAROLINA 29210
                                 (803) 951-1040

                                 WITH A COPY TO:

                              ELLEN J. ODONER, ESQ.
                           WEIL, GOTSHAL & MANGES LLP
                                767 FIFTH AVENUE
                            NEW YORK, NEW YORK 10153
                                 (212) 310-8000
            (Name, address and telephone number of person authorized
                     to receive notices and communications)

                               SEPTEMBER 11, 2004
             (Date of event which requires filing of this statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition that is the subject of this Schedule 13D, and is filing this
schedule because of Rule 13d-1(e), 13d-1(f) or 13d-1(g), check the following box
[ ].

     Note: Schedules filed in paper format shall include a signed original and
     five copies of the schedule, including all exhibits. See Rule 13d-7 for
     other parties to whom copies are to be sent.

                         (Continued on following pages)

                               (Page 1 of 6 Pages)





-------------------------------------------------------------              ---------------------------------------------------------
CUSIP No.  87927W10                                               13D                                                   Page 2 of 6
-------------------------------------------------------------              ---------------------------------------------------------
                                                                                                    
------------------------    --------------------------------------------------------------------------------------------------------
           1                NAME OF REPORTING PERSON                            PIRELLI & C. S.p.A.
                            I.R.S. IDENTIFICATION NO. OF ABOVE PERSON            Not Applicable
------------------------    -------------------------------------------------------------------------------------------------------
           2                CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP:                                          (a) [X]
                                                                                                                       (b) [ ]
------------------------    --------------------------------------------------------------------------------------------------------
           3                SEC USE ONLY
------------------------    --------------------------------------------------------------------------------------------------------
           4                SOURCE OF FUNDS:                                                  BK, WC
------------------------    --------------------------------------------------------------------------------------------------------
           5                CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
                            PURSUANT TO ITEM 2(d) OR 2(e):                                                                 [ ]
------------------------    --------------------------------------------------------------------------------------------------------
           6                CITIZENSHIP OR PLACE OF ORGANIZATION:                                             Italy
------------------------    --------------------------------------------------------------------------------------------------------

       NUMBER OF                     7               SOLE VOTING POWER:                                      47,155,300
         SHARES

      BENEFICIALLY           -------------------     -------------------------------------------------------------------------------
        OWNED BY                     8               SHARED VOTING POWER:                                  1,751,765,823
                                                                                                            (See Item 5)
          EACH               -------------------     -------------------------------------------------------------------------------
       REPORTING                     9               SOLE DISPOSITIVE POWER:                                 47,155,300

                             -------------------     -------------------------------------------------------------------------------
       PERSON WITH                  10              SHARED DISPOSITIVE POWER:                             1,751,765,823
                                                                                                            (See Item 5)
------------------------    --------------------------------------------------------------------------------------------------------
          11                AGGREGATE AMOUNT BENEFICIALLY OWNED BY REPORTING PERSON:                       1,798,921,123
                                                                                                            (See Item 5)
------------------------    --------------------------------------------------------------------------------------------------------
          12                CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES:                         [ ]
------------------------    --------------------------------------------------------------------------------------------------------
          13                PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11):                                       17.46%
                                                                                                                   (See Item 5)
------------------------    ------------------------------------------------------ -------------------------------------------------
          14                TYPE OF REPORTING PERSON:                              CO
------------------------    --------------------------------------------------------------------------------------------------------
                                       2

-------------------------------------------------------------              ---------------------------------------------------------
CUSIP No.  87927W10                                               13D                                                   Page 3 of 6
-------------------------------------------------------------              ---------------------------------------------------------

------------------------    --------------------------------------------------------------------------------------------------------
           1                NAME OF REPORTING PERSON                                 Olimpia S.p.A.
                            I.R.S. IDENTIFICATION NO. OF ABOVE PERSON                Not Applicable
------------------------    --------------------------------------------------------------------------------------------------------
           2                CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP:                                          (a) [X]
                                                                                                                       (b) [ ]
------------------------    --------------------------------------------------------------------------------------------------------
           3                SEC USE ONLY
------------------------    --------------------------------------------------------------------------------------------------------
           4                SOURCE OF FUNDS:                                                  WC
------------------------    --------------------------------------------------------------------------------------------------------
           5                CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
                            PURSUANT TO ITEM 2(d) OR 2(e):                                                                 [ ]
------------------------    --------------------------------------------------------------------------------------------------------
           6                CITIZENSHIP OR PLACE OF ORGANIZATION:                                             Italy
------------------------    -------------------     -------------------------------------------------------------------------------

       NUMBER OF                    7               SOLE VOTING POWER:                                          0
         SHARES
                            -------------------     --------------------------------------------------------------------------------
      BENEFICIALLY                  8               SHARED VOTING POWER:                                    See Item 5
        OWNED BY

          EACH              -------------------     --------------------------------------------------------------------------------
       REPORTING                    9               SOLE DISPOSITIVE POWER:                                     0


                            -------------------     --------------------------------------------------------------------------------
      PERSON WITH                  10              SHARED DISPOSITIVE POWER:                                See Item 5

------------------------    --------------------------------------------------------------------------------------------------------
          11                AGGREGATE AMOUNT BENEFICIALLY OWNED BY REPORTING PERSON:                        See Item 5
------------------------    --------------------------------------------------------------------------------------------------------
          12                CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES:                         [ ]
------------------------    --------------------------------------------------------------------------------------------------------
          13                PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11):                                     See Item 5
------------------------    --------------------------------------------------------------------------------------------------------
          14                TYPE OF REPORTING PERSON:                              CO
------------------------    --------------------------------------------------------------------------------------------------------


                                       3

           This Amendment No. 31 amends the Statement on Schedule 13D, dated
August 9, 2001, as amended (as previously amended, the "Statement on Schedule
13D"), filed by Pirelli S.p.A. (which, as reported in Amendment No. 21 to the
Statement on Schedule 13D, subsequently merged with and into Pirelli & C.
S.p.A., a company incorporated under the laws of the Republic of Italy), and,
commencing with Amendment No. 1 thereto, Olimpia S.p.A., a company incorporated
under the laws of the Republic of Italy, with respect to the ordinary shares,
euro 0.55 par value per share, of Telecom Italia S.p.A., a company incorporated
under the laws of the Republic of Italy. Capitalized terms used in this
Amendment without definition have the meanings ascribed to them in the Statement
on Schedule 13D.

           Pirelli & C., Olimpia, Edizione Holding and Edizione Finance, Hopa,
UCI and BCI are members of a group with respect to the Telecom Italia Shares.
This Amendment constitutes a separate filing on Schedule 13D by Pirelli & C. and
Olimpia in accordance with Rule 13d-1(k)(2) under the Securities Exchange Act of
1934. Pirelli & C. and Olimpia are responsible solely for the information
contained in their separate filing, except that information contained in the
Statement on Schedule 13D concerning any director or officer of Olimpia
nominated by Edizione Holding, Hopa, UCI or BCI has been provided by the
nominating person or by such nominee director or officer.

ITEM 6.    CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT
           ---------------------------------------------------------------------
           TO SECURITIES OF THE ISSUER
           ---------------------------

           Reference is made to the Shareholders Agreement (as that term is
defined in Item 3 of the initial Statement on Schedule 13D). On September 11,
2004, Pirelli & C., Edizione Holding and Edizione Finance published a notice in
Italy which reports that the term of the Shareholders Agreement has
automatically been renewed until October 4, 2007. A copy of the notice is filed
as Exhibit 64.

ITEM 7.    MATERIAL TO BE FILED AS EXHIBITS
           --------------------------------

64.        Notice of Pirelli & C., Edizione Holding and Edizione Finance, dated
           as  of  September 11, 2004.


                                       4

                                  EXHIBIT INDEX
                                  -------------

    Exhibit No.
    -----------

        64.      Notice of Pirelli & C., Edizione Holding and Edizione Finance,
                 dated as of September 11, 2004.











                                       5

                                   SIGNATURES
                                   ----------

           After reasonable inquiry and to the best knowledge and belief of the
undersigned, the undersigned certify that the information set forth in this
statement is true, complete and correct.

Date:    September 14, 2004

                                     PIRELLI & C. S.p.A.


                                     By:  /s/ Anna Chiara Svelto
                                          --------------------------------------
                                          Name: Anna Chiara Svelto
                                          Title:  Attorney-in-fact


                                     OLIMPIA S.p.A.


                                     By:  /s/ Luciano Gobbi
                                          --------------------------------------
                                          Name: Luciano Gobbi
                                          Title:  Director and Attorney-in-fact





                                       6