In this talk, I will try to answer the following questions:

- Why Sobolev spaces?

- What is a Sobolev space and what are its basic properties?

- Is there a Holder-type inequality for the product of two Sobolev functions?

- Some other questions that may come up.

Of course these results have long been known but I will mainly focus on some subtle points one should be careful about and results that may not be easily available in the literature.