Definition of a grammar I am learning about context free grammars and have been through few texts in a undetailed  manner  on these topic . I think I should know the exact , rigorous ,technical definition of what exactly a "grammar" means .

I could see that  ,in all of these lessons, a sequence of equations as follow :

 a = bc
 b = ed
 c = gh


I was tempted to conclude that "a grammar is a collection of symbols which are related by a set of equations which dictate rules for substitution of a symbol by a series of symbols "

Then I got to know that , not in all series of equations can we substitute one symbol by a series of another symbol .We can do it only in case of "context-free grammars " . 
Then I went through one of the stackexchange post and through a brilliant answer got to know what context free exactly means . 

So , I thought before I proceed ahead I better seek for the exact rigorous definition of a grammar . 
What exactly is the mathematical/technical definition of a grammar ?
A grammar is a set of production rules for symbol sequences.

But you knew that already. If you edit the question to make it more specific, we can offer more specific answers.