Major chords, together with the minor chords, are normally the first chords to learn on the guitar. These are fundamental and most other chords are extended or altered versions of major and minor chords.
Besides the basic major chords there are other categories that also use major in the name. Among these are major seventh, major ninth and major thirteenth.
Basic major chords
Major chord exercises (.pdf)
See also the most common progression involving major chords, the I - IV - V progression presented in all keys including pdf-files.
The chord names
The basic major chords are often written with single letters. Thus, the difference between C and C Major is, in this context, none. In some cases you may find these referred to as CM, DM, EM and so on. It matters if the "M" is uppercase or lowercase, in the latter case a minor chord is intended.
There are in total twelve different basic major chords, one for every pitch. Because of the standard tuning of the guitar, the root notes C#/Db, D#/Eb, F#/Gb, G#/Ab and A#/Bb are often found on less convenient positions at the fretboard (none of these tones can be played on an open string). This makes them harder to play and therefore less common. The five chords presented below are often played as barre chords or with a capo (click on the links below the pictures for further guidance).
The delta (triangle) symbol
Sometimes, especially in older notations, "major" can be represented by a delta symbol. The chord name in these cases include a letter followed by a tringle (often in superscript).
C△ (C triangle) = C major
Basic major chords with sharp or flat root
C# / Db
D# / Eb
F# / Gb
G# / Ab
A# / Bb
Theory of the major chords
A basic major chord always consists of three notes (or pitches). But since the guitar consists of six strings, some of the notes are unavoidably duplicated. The reason for this being the case is the instrument and its tuning. Normally, The G major is played on six strings and the D chord is played on only four. In the case of D major, the reason is that the root note D, that is played as the bass note, can't be found on the two lowest strings in this fret position.
All major chords are based on the major scale. The C major, C major 7th and so on are consequently based on the C major scale. This site doesn’t focus on scales, but you can find information on the subject elsewhere on the web, a recommended source is GuitarScale.org.
See also Chord progressions.
The Chord Chart Poster includes a selection of the 100+ most important chords for guitar.