What is the difference between savoir and connaître?

Savoir means to know in the sense of knowing how to do something e.g. a skill, knowing something by heart or knowing a fact.Je sais danser (I know how to dance).Je sais cette chanson (I know this song [I can sing the words by heart]).Je sais que la terre est ronde (I know that the earth is round). Connaître means to know in the sense of being acquainted with a person, place or thing. It is sometimes useful to translate it as to be familiar with e.g. il connaît Londres means he is familiar with London, he knows London.Je connais Luc (I know Luke [I am acquainted with Luke]).Je connais bien Paris (I know Paris well [Paris is very familiar to me]).Je connais cette chanson (I know this song [I have heard this song before]).