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I am new very new in this subject. I have a curiosity in understanding diff.geometry. I have some questions (which might sound elementary) to ask:

(1) Is diff.geometry a subject related to the study of surface, curvatures, manifolds?

(2) How it is different from Euclidean geometry?

(3) Is it that as General relativity deals with curved space time, hence differential geometry comes into the scene?

(4) Does it include differential calculus and 3-d geometry?

Thanks