There are many different types of Analysis'. Calculus is usually called "Real Analysis" because you use real (i.e. non imaginary) numbers.
There is another one called Complex Analysis. That one does Calculus with complex (imaginary) numbers.
The Greek translation is "study of space". That is basically what it is. It studies objects in space in a mathematical way. For example, what does it means a "region" how do you define that. And what does it means "inside of a circle". How do you define that? And similar related things. It is also very very huge.What is Topology?
Analysis and Topology are seperate areas of mathematics.
Now the funny thing is that out of all the places you could have placed this thread you placed it in "Algebra", which is a totally different area from Analysis and Topology. (Algebra is my favorite).