+This section introduces having more than one note at the same time:
+multiple instruments, multiple staves for a single instrument (i.e. piano),
+and chords.
+
+Polyphony in music refers to having more than one voice occurring in
+a piece of music. Polyphony in LilyPond refers to having more than
+one voice on the same staff.
+
+@menu
+* Music expressions explained::
+* Multiple staves::
+* Piano staves::
+* Single staff polyphony::
+* Combining notes into chords::
+@end menu
+
+
+@node Music expressions explained
+@subsection Music expressions explained
+
+In LilyPond input files, music is represented by @emph{music
+expressions}. A single note is a music expression, although it is not
+valid input all on its own.
+
+@lilypond[quote,ragged-right,verbatim,fragment,relative=2]
+a4
+@end lilypond
+
+Enclosing a group of notes in braces creates a new music expression:
+
+@lilypond[quote,ragged-right,verbatim,fragment,relative=2]
+{ a4 g4 }
+@end lilypond
+
+Putting a group of music expressions (e.g. notes) in braces means that
+are in sequence (i.e. each one follows the previous one). The result
+is another music expression:
+
+@lilypond[quote,ragged-right,verbatim,fragment,relative=2]
+{ { a4 g } f g }
+@end lilypond
+
+@subheading Simultaneous music expressions: multiple staves
+
+This technique is useful for polyphonic music. To enter music
+with more voices or more staves, we combine expressions in
+parallel. To indicate that two voices should play at the same time
+simple enter a simultaneous combination of music expressions. A
+@q{simultaneous} music expression is formed by enclosing expressions inside
+@code{<<} and @code{>>}. In the following example, three sequences (all
+containing two separate notes) are combined simultaneously:
+
+@lilypond[quote,ragged-right,verbatim]
+\relative c'' {
+ <<
+ { a4 g }
+ { f e }
+ { d b }
+ >>
+}
+@end lilypond
+
+Note that we have indented each level of the input with a different
+amount of space. LilyPond does not care how much (or little) space there
+is at the beginning of a line, but indenting LilyPond code like this makes
+it much easier for humans to read.
+
+@subheading Simultaneous music expressions: single staff
+
+To determine the number of staves in a piece, LilyPond looks at the first
+exression. If it is a single note, there is one staff; if there is a
+simultaneous expression, there is more than one staff.
+
+@lilypond[quote,ragged-right,verbatim]
+\relative c'' {
+ c2 <<c e>>
+ << { e f } { c <<b d>> } >>
+}
+@end lilypond
+
+@cindex expression
+@cindex music expression
+@subheading Analogy: mathematical expressions
+
+This mechanism is similar to mathematical
+formulas: a big formula is created by composing small formulas. Such
+formulas are called expressions, and their definition is recursive so
+you can make arbitrarily complex and large expressions. For example,