Chord functions

Out of the seven diatonic notes of a given key grouping them into triades (1st degree + 3rd degree + 5th degree), we can build three Major and three minor chords. In context of that given key these six chords are assigned harmonic functions. In the key of C-major these functions are:

C : I the tonic chord (C-E-G)
Dm: ii  supertonic (rarely referred by this name in this book) (D-F-A)
Em: iii mediant (rarely referred by this name in this book) (E-G-B)
F : IV  subdominant (F-A-C)
G : V  dominant (G-B-D)
Am: vi submediant (rarely referred by this name in this book) (A-C-E)

These are the so-called diatonic chord funstions. See for example "One Year Of Love" where you'll see this six basic chords in the homekey of this song. Bob Dylan's classic album "Blonde On Blonde" features almost exclusively basic diatonic chords. 
In nearly all Queen songs you'll find non diatonic chords as well. For example the C chord in the "Fat Bottomed Girls" which is in D-Major. The tonic chord often opens the song and closes it, which helps one getting oriented harmony-wise.

 

Chord functions in a-minor:

Am: i   tonic
C : III
Dm: iv 
Em: v   dominant
E : V   dominant
F : VI
G : VII

 

Note the capitals refer to Major chords. The minor function will be rarely referred by name in this book.

The song analyses will dispaly the chords of the song bar by bar. These bars are grouped in phrases. The phrases are grouped in sections.
 Below the traditional name of the chord you will see the function number (roman number). For example the "mama just killed a man..." phrase off "Bohemian Rhapsody" will look like this (four bars):

| Eb  | Cm   | Fm   | - Bb |
| I   | vi   | ii   | - V  |

The "-" means that the previous chord is sustained in the first half of the fourth measure.