Rhythm is the organisation of groups of accented and unaccented beats at a specific tempo.
Rhythm is discrete unpitched sound not continuous unpitched sound. This is a feature that distinguishes rhythm from some types of noise. Noise can be continuous or discrete; rhythm is always discrete. Continuous sound does not, and cannot, have a rhythm, there must be a discrete element of some sort in order for it to be rhythm. This discrete element is called a beat.
Rhythm is something that can be felt as well as heard. You can feel the rhythm of your heartbeat and your pulse, for instance. This is inaudible rhythm. We, however, are interested in audible rhythm, rhythm that we can hear. So writing rhythm means writing it as audible unpitched sound.
Rhythm forms patterns that recur or repeat over time. This is a little vague but it will do for starters. We will be more precise as the guide progresses.
To sum up, rhythm is audible unpitched sound with a beat that forms recurring patterns over time.
Now to look at how to write it. The guide starts with a look at how rhythm is generated with a percussion instrument. We then analyse the basic elements of rhythm, in particular, meter, and see how they can be built up into rhythm patterns starting with simple patterns and evolving into more complex shapes. We end by looking at the differences between pitch and rhythm, which provides an entree to the worlds of melody and harmony.