This puzzle is a variant of U-Bahn with stations. The rules originate from a series by tuace.
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.
Cells with circled numbers are stations. Draw a non-intersecting path through the centers of some cells, which travels through every station in ascending order. The path must lie entirely on the loop network.
Between any two consecutive stations, the length of the path must equal the taxicab distance between the two stations.