Qt is a cross-platform application development framework widely used for the development of application software that can be run on various software and hardware platforms with little or no change in the underlying codebase, while having the power and speed of native applications. Qt is available with both commercial and open source licenses. Questions about programming with Qt should be asked on Stack Overflow.
Qt (pronounced officially as cute (/kyut/) though commonly pronounced as Q.T. (/ˈkyu ti/)) is a cross-platform application development framework widely used for the development of GUI programs (where it functions like a cross-platform widget toolkit), and also used for developing non-GUI programs such as console tools and servers. wikipedia
Qt was created by Trolltech, and was acquired by Nokia in 2008. One month after the end of symbian development at Nokia, Nokia decided to sell Qt. From September 2012 and until now Qt is managed by the Qt Company which is subsidiary of Digia.
Note that questions about programming with Qt should be asked on Stack Overflow, since programming questions are off-topic for Super User.