# Confusions regarding convolution?

As far as i have studied and understood, convolution is the process by which we can get/determine output of LTI systems While reading one web link about convolution, i came across certain notation ,that i couldn't understand as shown highlighted in attached photo

1)Are these notations referring to delay/shift in input and impulse response?

2)Also it mentions that **Periodic or circular convolution is also called as fast convolution as shown highlighted in last line of 2nd photo attached. Is it idea correct?**