a knot homology theory associates to a knot or link a chain complex whose graded euler characteristic is a classical knot polynomial. this type of knot invariant has been increasingly influential in low-dimensional topology since the first one was defined in 1999. this primarily expository talk will introduce some knot homology theories with an emphasis on the commonalities in their constructions and their relationships to other areas in mathematics (symplectic geometry, representation theory, etc.). towards the end, we will encounter some areas of current research. no significant knowledge of low-dimensional topology will be assumed. the talk should be accessible to beginning graduate 2022年亚洲世界杯预选赛 , but hopefully still interesting to those who are further along!