Abstract: An underground, on-ground or over-ground public transportation train-like vehicle that can move both on steep-slope terrain and horizontal or semi-horizontal terrain along a straight line or almost straight line route when seen from above, while remaining always in the same train configuration, enabling so the passengers to stay all the time in the same vehicle while moving between any two points at the same or different levels of a hilly city using the shortest in distance and time route, independently of weather conditions. A mobile cabin-to-cabin attachment enables the cabins of said train-like vehicle to vertically displace each with respect to the other and to horizontally rotate each with respect to the other, making thus possible for the passengers to remain in always-upright position and for the vehicle to move on a terrain with constantly changing slope, even when this change is abrupt, and not only along an ideally straight line. A 45.degree.