GNOME-DB used to be composed of several components, not all of them being mandatory: libgda, libgnomedb, and mergeant. All of these components have been grouped into one single source package with optionnal compilation of the UI part (so it's still possible to restrict the compilation to the core, non UI part).
libgda has been developped primarily on a Linux OS, but compiles and runs on any Unix system where all their dependencies have been installed (MacOSX included). Starting with version 4.0.0, Microsoft Windows is also supported, please see the GnomeDB on Windows page for more information about that platform (including compiling instructions).
Linux / Unix
This page does not contain any binary distribution of Gnome-DB. Refer to the packages offered by the Linux distribution to install Gnome-DB (I can add links to externally made binary packages, though).
However some Linux distributions contain already installable packages, which can easily be installed.
As an exercice, some MS Windows packages have been made available at http://download.gnome.org/binaries/win32/libgda
A new installer for the GdaBrowser and additional tools (using the NSIS builder) is now available at http://www.gnome.org/~vivien/GdaBrowserSetup.exe. It has been tested on Windows XP and Windows 7; please report any bug you find. Its SHA256 sum is c7e15d6343d4b2e58d3c07305d859119a2a4abfa7c94e2f9c3160c92059f3e36.
Some additional information can be found at http://www.gnome.org/~vivien.
Compilation for Windows has been extremely simplified by using docker images, see the scripts to build and use them in Libgda's sources.
The current stable version of libgda is 5.2, available at: http://ftp.gnome.org/pub/GNOME/sources/libgda/5.2/
See the Roadmap form more information about the current development version and the changes.
Libgda is hosted by GNOME's infrastructure, and its git repository is available at: http://git.gnome.org/browse/libgda