A shoe comprising: a) a shaft arrangement and a sole, wherein: b) the shaft arrangement has b.1) an outer shaft material and b.2) an air-permeable layer arranged in a shaft bottom; c) the air-permeable layer is arranged in a lower area of the shaft arrangement on the sole side above the sole; d) the air-permeable layer has a three-dimensional structure that permits air passage at least in horizontal direction; and e) the outer shaft material has at least one air-passage opening in a lower peripheral area on the sole side, which opening connects the air-permeable layer to the outer surroundings in such a way that air can be exchanged between the outer surroundings and the air-permeable layer, f) wherein a waterproof, water vapor-permeable functional layer (34, 38) is provided in a lower area of the shaft arrangement that faces the sole, the air-permeable layer being arranged beneath the functional layer (34, 38), g) wherein the air-permeable layer is embodied as an air-permeable spacer structure, which forms an upper and a lower support surface spaced from each other, h) wherein the two support surfaces are each formed by a sheet-like structure, which are connected to each other in air-permeable and spaced apart manner by means of mono- or multifilaments or fibers, at least the upper one of the sheet-like structures being air permeable and constructed with an open-pore woven, knit or warp-knit textile material, with the air permeable layer containing an air volume of at least 50%. a) a shaft arrangement and a sole, wherein: b) the shaft arrangement has b.1) an outer shaft material and b.2) an air-permeable layer arranged in a shaft bottom; c) the air-permeable layer is arranged in a lower area of the shaft arrangement on the sole side above the sole; d) the air-permeable layer has a three-dimensional structure that permits air passage at least in horizontal direction; and e) the outer shaft material has at least one air-passage opening in a lower peripheral area on the sole side, which opening connects the air-permeable layer to the outer surroundings in such a way that air can be exchanged between the outer surroundings and the air-permeable layer, f) wherein a waterproof, water vapor-permeable functional layer (34, 38) is provided in a lower area of the shaft arrangement that faces the sole, the air-permeable layer being arranged beneath the functional layer (34, 38), g) wherein the air-permeable layer is embodied as an air-permeable spacer structure, which forms an upper and a lower support surface spaced from each other, h) wherein the two support surfaces are each formed by a sheet-like structure, which are connected to each other in air-permeable and spaced apart manner by means of mono- or multifilaments or fibers, at least the upper one of the sheet-like structures being air permeable and constructed with an open-pore woven, knit or warp-knit textile material, with the air permeable layer containing an air volume of at least 50%. b) the shaft arrangement has b.1) an outer shaft material and b.2) an air-permeable layer arranged in a shaft bottom; b.1) an outer shaft material and b.2) an air-permeable layer arranged in a shaft bottom; c) the air-permeable layer is arranged in a lower area of the shaft arrangement on the sole side above the sole; d) the air-permeable layer has a three-dimensional structure that permits air passage at least in horizontal direction; and e) the outer shaft material has at least one air-passage opening in a lower peripheral area on the sole side, which opening connects the air-permeable layer to the outer surroundings in such a way that air can be exchanged between the outer surroundings and the air-permeable layer, f) wherein a waterproof, water vapor-permeable functional layer (34, 38) is provided in a lower area of the shaft arrangement that faces the sole, the air-permeable layer being arranged beneath the functional layer (34, 38), g) wherein the air-permeable layer is embodied as an air-permeable spacer structure, which forms an upper and a lower support surface spaced from each other, h) wherein the two support surfaces are each formed by a sheet-like structure, which are connected to each other in air-permeable and spaced apart manner by means of mono- or multifilaments or fibers, at least the upper one of the sheet-like structures being air permeable and constructed with an open-pore woven, knit or warp-knit textile material, with the air permeable layer containing an air volume of at least 50%.