Dotted Rhythms
Dotted rhythms are rhythms in which at least one note is dotted. This means that a dot is placed immediately after the note.

This dot indicates that the note's duration is extended by half of its original value:

A quarter note therefore becomes a quarter note with an additional eighth note. This note has a duration of 1/2 + 1/4 of a beat.
A dotted half note, on the other hand, becomes a half note with an additional quarter note:

This note therefore lasts 3 beats.
Double Dots
There is also the possibility of using double dots. In this case, two dots are placed after the note. They extend the note by half of its original value, and this additional half is then extended by another half through the second dot:

However, this variation is less common than single dotting.