The Major Scale

Improvisation, and music in general, is based upon the idea of repetition and variation. It's underlying psychological truth is the fact that people are able to process only small chunks of information. In order for such a chunk to become interesting it has to be presented repeatedly, but each time slightly different, lest it became boring.
Thus arises the idea of structure: the blueprint of repeating and varying musical ideas.
The first important implementation of the idea of structure in music is the concept of playing subsets of the available notes. These are called scales. The most relevant scale to the western music is the major scale, characterized by the following interval formula: whole-tone, whole-tone, half-tone, whole-tone, whole-tone, whole-tone, half-tone.

Here is the scale in all positions on the fretboard: