A chord is a group of notes played together. The lowest note is usually the root. The root defines the name of the chord (for example, C is the root of a C major chord).
From the root, we build chords by counting steps called intervals.
An interval is the distance between two notes. We count using half-steps (semitones). One semitone is the smallest step on a piano, moving from one key to the very next.
We use formulas to build chords from intervals. Numbers mean semitone distances:
A flat (♭) means the note is shifted one semitone down. A sharp (♯) means the note is shifted one semitone up.
A double flat (♭♭) means the note is shifted two semitones down.
Different chords carry different moods. Here are common associations: