FAT is a File System created by Microsoft in 1977.
Simple and not formally defined at the beginning it became quite complex but loosely defined and actually ruled by Microsoft's implementation.

References

• The FAT part of the GNU Parted documentation
  This gives an good overview of FAT file system and is one of the only documentations to detail Microsoft kludges in FAT12 and FAT16. It also corrects some wrong information of other documentations.
  
• File Systems: http://perso.orange.fr/pierrelib/filesystems/ (2001-11-24)
  • FAT16: http://perso.orange.fr/pierrelib/filesystems/fat16.html with references from Microsoft Knowledge Base:
    • Windows NT Boot Process and Hard Disk Constraints (Last Review: May 6, 2003)
    • Detailed Explanation of FAT Boot Sector (Last Review: December 6, 2003)
    • Standard Floppy Disk Formats Supported by MS-DOS (Last Review: May 12, 2003)
    • FAT Type and Cluster Size Depends on Logical Drive Size (Last Review: November 16, 2006)
  • FAT32: FAT32 File System Specification (PDF by Microsoft, 2000-12-06)
  • VFAT Long File Names (LFNs): http://perso.orange.fr/pierrelib/filesystems/vfat.html
    NOTE: Some informations here are missing (the 2 byte fields "is_upper_case_name" at offset 12 and "creation_time_low" at offset 13) and can be found in GNU Parted documentation. The final discussion is quite useless.
    
• Microsoft explains How FAT Works in Windows Server 2003 (Updated: March 28, 2003)
• Default cluster size for FAT and NTFS

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