Originally Posted by: BlochCan anyone give a simple introduktion to the mathematics of the Fret Board, and how to use it, - especially in a solo, when to follow different chords?

Start with GF2, at the lesson on intervals:

http://www.guitartricks.com/course.php?input=2

Keep hitting the next button and that will eventually take you into scales & chords!

The basics of improvisation (how to play over chord changes in a solo) are here:

Introduction To Improvisation For Beginners
http://www.guitartricks.com/tutorial.php?input=876

Introduction To Improvisation In A Major Key
http://www.guitartricks.com/tutorial.php?input=483

Introduction To Improvisation In A Minor Key
http://www.guitartricks.com/tutorial.php?input=491

If you are interested in mapping out (visualizaing) the entire fretboard try these:

Major Scale Patterns And Positions
http://www.guitartricks.com/tutorial.php?input=453

Minor Scale Patterns And Positions
http://www.guitartricks.com/tutorial.php?input=887

Let me know if these help or you are after something else. Have fun!