Tie
A tie is a curved line joining two notes of the same pitch into one longer sound. The second note is not played again: you simply keep holding the key.
Two quarter notes joined by a tie sound like one half note: press once and hold for two beats. A half note tied to a quarter note lasts three beats. The tie is drawn from one notehead to the next.
Where a tie is really needed is at a bar line. A note cannot cross the bar line — each measure keeps its own beats. So two notes are written, one on each side, and tied together: that is the only way to hold a sound over a bar line.
Do not confuse a tie with a slur. A tie always joins two notes of the same pitch. A curve over different notes is not a tie but a slur: it tells you to play them smoothly, legato, each note still struck.
What it sounds like
A tie does not change the note — it only lengthens the sound. The ear hears one long note where the eye sees two.
Where it is taught: the studio’s interactive textbook, chapter 12, “Eighth notes and the dotted quarter” and chapter 13, “Ties, rests and the pickup”.