Your "Introduction to Musical Rhythm" includes this remark:

"A quarter-note` or `crotchet` lasts for 1 beat"

Obviously this is not necessarily true. A time signature of 2/2 suggests groupings of two beats, one half note each in duration; a time signature of 6/8 suggests groupings of two beats, one dotted quarter note each in duration; and so on--which is not to say that the time signature decides the matter; the actual music decides the matter (subject to subjective interpretation, which is what beat necessarily is); the time signature, as I say, only SUGGESTS the duration of the beat.

The sort of misinformation we find in a remark such as "a quarter-note` or `crotchet` lasts for 1 beat" can do long-lasting damage and will at the very least impede the growth of musical understanding. Please change it. You can simply say instead that a quarter note lasts half as long as a half note or one fourth as long as a whole note, which is all the beginner needs to know at this point.

Thank you.