This puzzle is a variant of U-Bahn. If you are unfamiliar with U-Bahn, here is a guide that covers the core logic.
Draw a loop network through the centers of some cells, which may branch or turn, but may not have any dead ends.
A clue outside the grid indicates how many times the corresponding line shape (i.e. a cross, branch, straight line, or turn) appears in the corresponding row or column, irrespective of the line shape's rotation.
Within a cage, any cells that are visited by the loop network must have the same line shape, irrespective of rotation. Different cages may have different line shapes, and cages may be empty.