One of the most efficient ways to memorize scales and play them on the guitar is using box patterns. These are ways of 'mapping' the scale across the guitar fretboard, creating fixed shapes that can be transposed to play the scale in a different key. They are particularly helpful for improvisation, and once they are memorized, they serve as an excellent aid to understand the visual and auditory relationships between intervals. Select a root note to see a list of box patterns for the major scale:
The Dorian or Doric mode, in modern music theory, is a modal diatonic scale. It corresponds to the white keys of the piano from D to D or any transposition of this WHWWWHW intervallic pattern (with H meaning haf-tone and W meaning whole tone). Though historically different, it can be seen as a minor scale with its sixth grade ascended, and it is often considered as an offshot of the minor scale. It is usually used as a compositional device for deviating from the traditional minor sound, as the ascended sixth creates a IVM chord, and a somewhat medieval-like sound in melodies.
The dorian mode is named after the dorian greeks (an ethnic group of the ancient greek people, together with the aeolians, achaeans and ionians). Somewhat confusingly, the term dorian was applied to a number of different scales historically (since the modern naming system we use for modes is actually the result of a series of interpretations and sometimes wrong translations carried out by music theorists of the middle ages). For example, it is believed that one of the uses of the term dorian in greek music referred to what we today know as phrygian scale.
There are a number of famous compositions in dorian mode: Drunken sailir, Maiden Voyage (by Herbie Hancock), Milestones (by Miles Davies), etc.