From Wikipedia: "Integrated Services Digital Network (ISDN) is a set of communication standards", and for DSL: "Digital subscriber line is a family of technologies". My question is: Is DSL built on top of ISDN and what are the differences? I am a bit confused, since both describe ways of transmitting data over telephone lines.
You can't really compare those two technologies.
ISDN is a network protocol encompassing practically the whole OSI model from physical to application layer.
xDSL is a family of physical-layer line protocols running between two interfaces (point-to-point). There are ADSL and VDSL variants that allow the co-existence with POT and ISDN on the same line using a frequency splitter. This is often called DSL over ISDN, but it's actually more DSL besides ISDN because the ISDN (or POTS) doesn't know a thing about DSL.