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I have seen in Thinking of Lie derivative for the first time that one way to think of differentiating a vector field with respect to another vector field is the Lie derivative $L_XY$.

Now, given vector fields $X$ and $Y$ there is another notion of differentiation called the covariant differentiation $\nabla_XY$. What does this do which lie derivative could not do.

Please try to give broad picture than some calculations. Any references are most welcome.

EDIT : The question which John Ma linked does not really answer this question. That question is useful for some one who already know what is lie/covariant/exterior derivative and says how do you relate these. But, what I am asking is some thing else and I do not really know what is covariant derivative and I want to think of covariant derivative in lines of Thinking of Lie derivative for the first time

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