UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 13F

                               FORM 13F Cover Page

        Report for the Calendar Year or Quarter Ended: September 30, 2004

Check here if Amendment:           |_|; Amendment Number: ____

This Amendment (Check only one):   |_| is a restatement
                                   |_| adds new holding entries.

Institutional Manager Filing this Report:

Name:     Two Sigma Investments, LLC

Address:  379 West Broadway
          5th Floor
          New York, New York 10012

13F File Number: 28- 10385

The institutional investment manager filing this report and the person by whom
it is signed hereby represent that the person signing the report is authorized
to submit it, that all information contained herein is true, correct and
complete, and that it is understood that all required items, statements,
schedules, lists, and tables, are considered integral parts of this form.

Person Signing this Report on Behalf of Reporting Manager:

Name:   Mark Pickard
Title:  President
Phone:  (212) 625-5731

Signature, Place and Date of Signing:

    /s/ Mark Pickard            New York, New York           November 15, 2004
-----------------------     --------------------------     ---------------------
     [Signature]                   [City, State]                   [Date]


Report Type: (Check only one):

[X]  13F HOLDINGS REPORT. (Check here if all holdings of this reporting manager
     are reported in this report).

[_]  13F NOTICE. (Check here if no holdings reported are in this report, and all
     holdings are reported by other reporting managers(s).)

[_]  13F COMBINATION REPORT. (Check here if a portion of the holdings for this
     reporting manager are reported in this report and a portion are reported by
     other reporting manager(s).)


                              Form 13F SUMMARY PAGE

Report Summary:

Number of Other Included Managers:       0

Form 13F Information Table Entry Total:  0

Form 13F Information Table Value Total: $0
                                         (thousands)

Confidential information has been omitted from this public Form 13F report and
filed separately with the Securities and Exchange Commission.

List of Other Included Managers:

Provide a numbered list of the name(s) and Form 13F file number(s) of all
institutional investment managers with respect to which this report is filed,
other than the manager filing this report.

No.            Form 13F File Number          Name

1.             28-10704                      Two Sigma Equity Portfolio, LLC
----           ---------------------         --------------------------------



                                                    FORM 13F INFORMATION TABLE

                                                    Two Sigma Investments, LLC
                                                        September 30, 2004

COLUMN 1                COLUMN  2      COLUMN 3     COLUMN 4            COLUMN 5        COLUMN 6  COLUMN 7       COLUMN 8
---------------     --------------   -----------   ---------     -------------------  ----------- --------- --------------------
                                                     VALUE        SHRS OR   SH/ PUT/   INVESTMENT  OTHER      VOTING AUTHORITY
NAME OF ISSUER      TITLE OF CLASS      CUSIP       (X$1000)      PRN AMT   PRN CALL   DISCRETION  MANAGERS  SOLE  SHARED  NONE
---------------     --------------   -----------   ---------     -------------------  ----------- --------- --------------------
                                                                                           
    None                 None             None         0             0       0    0        None       1        0      0     0


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