What is Task Manager?
A task manager is a software utility to manage day to day activity. It helps achieve specific goal or goals of individuals or groups. These software are useful for individuals working on project or groups of individuals collaborating and sharing knowledge and work for the accomplishment of collective goal(s).

What is GTD?
From Wikipedia:

Getting Things Done (GTD) is an organizational method created by David Allen, described in a book of the same name.
The Getting Things Done method rests on the principle that a person needs to move tasks out of the mind by recording them externally. That way, the mind is freed from the job of remembering everything that needs to be done, and can concentrate on actually performing those tasks.

GeeTeeDee (v0.1.175)


GeeTeeDee is a GTD compliant software developed by Codea. It features a fancy and fairly modern interface.

PROS:

• Fancy and elegant design
• Ability to group tasks
• Drag and Drop for shorting and moving task between groups.
• Switchable to compact view
• Friendly and quick installation
• Updates regularly
• Portable version available (Windows only), since version 0.1.161

CONS:

• Confusing for beginners
• No context menu
• Not low on memory (as the official website says it as lightweight)
• Require "Get Used To"
• No help or "Getting Started With" online or offline

Getting GeeTeeDee:

GeeTeeDee is available for Windows as well as Linux (for Debian and RPM base distros).
Download for Windows from THIS page.
Note: Portable version is for Windows (only).

For getting and installing on Linux based distribution head towards THIS page.

GeeTeeDee
Website: http://codea-dev.com/gtd/