I heared that Eclipse has its own graphics library, SWT.
Yup, it does indeed. Developed by IBM for the Eclipse project, along with another library called JFace which is built ontop of SWT.
Does this influence the GUI development with Eclipse ? Can't I develop AWT or Swing applications with Eclipse ?
No it has no influence at all, any applications you write using Eclipse will uses whatever toolkit you you use. The only direct influence there is, is if you want to write a plugin for Eclipse. In that case there is a diffenrence and its more preferable to use SWT / JFace, BUT you could use AWT/Swing if you wanted.
Is it possible to export SWT library and use it in client deployments
You don't even need to export it, if you goto the eclipse downloads page and goto a release page (for instance for 2.1.1:
http://download.eclipse.org/downloads/drops/R-2.1.1-200306271545/index.php ), scroll to the bottom of the page and you will find a section called "SWT Binary and Source" just choose the one appropriate for your platform.
Rob
