If cosets $xH \ne Hy$ then, their intersection is empty? I am revising basic Group Theory and was hoping to check if my understanding about this is correct.
http://www.proofwiki.org/wiki/Left_and_Right_Coset_Spaces_are_Equivalent says that the left and right coset spaces are equivalent.
Does this mean if cosets $xH \ne Hy$ then, their intersection is empty?

No, it means that there is a bijection between the set of left cosets and the set of right cosets. It is entirely possible that $xH\neq Hy$ yet their intersection is nonempty. For example, for a non-normal subgroup $H$ we have $xH\neq Hx$ for some $x$ yet $x\in xH\cap Hx$.
