I worked from this book extensively during my undergraduate thesis, and it was an absolute joy to read and learn from. Compared to Lickorish ("An Introduction To Knot Theory"), the explanations were easy even if you hadn't had 3 semesters of graduate abstract algebra.
If you want a fun application of where knot theory can be used "in the real world" there are some interesting applications to DNA untangling and the function of DNA Topoisomerase - e.g.:
https://sinews.siam.org/Details-Page/untangling-dna-with-kno...