Grammar includes Syntax (rules of sentence structure) and Transformations (the rules to change that structure).
When I think of Grammar, I think of two things--Syntax, the rules of Structure; and Transformations, the rules to change that structure.
Structure Rules: In the real world, we are often wanting to communicate about someone who is doing something to someone else or something, somewhere at sometime.
There are two structural systems that languages may use to communicate these relationships.
These are Inflectional and/or Analytic systems.
Inflectional Languages: One method is by using bound morphemes to create different word endings (inflections) to reflect these relationships. Languages that rely heavily on this are called Inflectional Languages.
Russian is a fine example of a language that is highly inflectional. For example the word cat (kashka) has the inflection "a" on the end. This means the cat is the actor.
NOTES: Some more information on structure in language.