Knotting, as the 11
th of
the
39 Melachot constitutes of the
tying any
permanent knot.
Tying a bow, however, is permitted, as it
is easily undone with one hand.
Therefore, one may
tie shoes on
Shabbat.
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Most of this information is taken
from the book "SABBATH Day of Eternity"
by Rabbi Aryeh Kaplan, published by NCSY.
In the book itself, there are notes that refer the
reader to detailed footnotes.
I am lucky to have found such a clear, concise manual
with these brief overviews of laws so vast and complex
there are Rabbis that specialize in them.