I suppose Differential Geometry is useful in numerous things from engineering to architecture to construction or aviation, depending on what you are seeking to use it for, or you can just fall in love with the beauty of geometry as a system, and in that context it, alongside mathematics, becomes a game of Sudoku, a very very addictive hobby.
I have my own method for understanding and enjoying geometry, basically you take the 1D point, and turn it into all 2D shapes, square, circle, triangle, oval, rectangle, hexagon etc, which you then turn into all 3D shapes, and then into all their higher dimensional forms from 2D to 5D etc, and then you take all these shapes from 2D to the highest dimension beyond 3D and then view them in 3D, 4D, 5D and so on, "space"-i.e. you currently view a cube(a 3D square) in 3dimensional space- this produces a wide variety of geometric structure's and then with all these shapes, you then begin to understand such things as topology, manifolds, homeopathic, area, square root, angles etc. Geometry when you crack the pattern is a beautiful system.
