What's the difference between theorem, lemma and corollary? Can anybody explain me what is the basic difference between theorem, lemma and corollary? 
We have been using it for a long time but I never paid any attention. I am just curious to know.

Terence Tao (Analysis I, p. 25, n. 4):

From a logical point of view, there is no difference between a lemma, proposition,
  theorem, or corollary - they are all claims waiting to be proved. However, we use
  these terms to suggest different levels of importance and difficulty.
A lemma is an easily proved claim which is helpful for proving other propositions and theorems, but is usually not particularly interesting in its own right.
A proposition is a statement which is interesting in its own right, while
a theorem is a more important statement than a proposition which says something definitive on the subject, and often takes more effort to prove than a proposition or lemma.
A corollary is a quick consequence of a proposition or theorem that was proven recently.

