Sensor arrangement for detecting surface stresses and/or the microstructure state of a ferromagnetic workpiece, characterized in that - at least one first basic coil system (1, 22a, 32a, 42a) which is arranged in a first direction and has a first directional sensitivity is provided, wherein the first basic coil system (1, 22a, 32a, 42a) comprises at least one excitation coil and a receiver coil on a common ferrite core for magnetically permeating a surface of the workpiece in a direction-sensitive manner and for determining the permeability in a direction-dependent manner, - at least one second basic coil system (2, 22b, 32b, 42b) which is arranged in a second direction and has a second directional sensitivity is provided, wherein the second basic coil system (2, 22b, 32b, 42b) comprises at least one excitation coil and a receiver coil on a common ferrite core for magnetically permeating a surface of the workpiece in a direction-sensitive manner and for determining the permeability in a direction-dependent manner, - at least one third basic coil system (3, 22c, 32c, 42c) which is arranged in a third direction and has a third directional sensitivity is provided, wherein the third basic coil system (3, 22c, 32c, 42c) comprises at least one excitation coil and a receiver coil on a common ferrite core for magnetically permeating a surface of the workpiece in a direction-sensitive manner and for determining the permeability in a direction-dependent manner, - and wherein at least the first basic coil system (1, 22a, 32a, 42a) and the second basic coil system (2, 22b, 32b, 42b) form a first differential angle (α1) and the second basic coil system (2, 22b, 32b, 42b) and the third basic coil system (3, 22c, 32c, 42c) form a second differential angle (β1), - wherein the first basic coil system (1, 22a, 32a, 42a) is arranged outside the second directional sensitivity and the third directional sensitivity, the second basic coil system (2, 22b, 32b, 42b) is arranged outside the first directional sensitivity and the third directional sensitivity and the third basic coil system (3, 22c, 32c, 42c) is arranged outside the first directional sensitivity and the second directional sensitivity, - and wherein the sensor arrangement is constructed in such a manner that the coil axes of the first basic coil system (1, 22a, 32a, 42a), of the second basic coil system (2, 22b, 32b, 42b) and of the third basic coil system (3, 22c, 32c, 42c) are oriented orthogonally with respect to the surface of the workpiece during measurement, - with the result that an independent measured value for determining a complete internal stress tensor can be obtained by means of each basic coil system, from which the mechanical surface stresses of the workpiece can be at least partially determined. - at least one first basic coil system (1, 22a, 32a, 42a) which is arranged in a first direction and has a first directional sensitivity is provided, wherein the first basic coil system (1, 22a, 32a, 42a) comprises at least one excitation coil and a receiver coil on a common ferrite core for magnetically permeating a surface of the workpiece in a direction-sensitive manner and for determining the permeability in a direction-dependent manner, - at least one second basic coil system (2, 22b, 32b, 42b) which is arranged in a second direction and has a second directional sensitivity is provided, wherein the second basic coil system (2, 22b, 32b, 42b) comprises at least one excitation coil and a receiver coil on a common ferrite core for magnetically permeating a surface of the workpiece in a direction-sensitive manner and for determining the permeability in a direction-dependent manner, - at least one third basic coil system (3, 22c, 32c, 42c) which is arranged in a third direction and has a third directional sensitivity is provided, wherein the third basic coil system (3, 22c, 32c, 42c) comprises at least one excitation coil and a receiver coil on a common ferrite core for magnetically permeating a surface of the workpiece in a direction-sensitive manner and for determining the permeability in a direction-dependent manner, - and wherein at least the first basic coil system (1, 22a, 32a, 42a) and the second basic coil system (2, 22b, 32b, 42b) form a first differential angle (α1) and the second basic coil system (2, 22b, 32b, 42b) and the third basic coil system (3, 22c, 32c, 42c) form a second differential angle (β1), - wherein the first basic coil system (1, 22a, 32a, 42a) is arranged outside the second directional sensitivity and the third directional sensitivity, the second basic coil system (2, 22b, 32b, 42b) is arranged outside the first directional sensitivity and the third directional sensitivity and the third basic coil system (3, 22c, 32c, 42c) is arranged outside the first directional sensitivity and the second directional sensitivity, - and wherein the sensor arrangement is constructed in such a manner that the coil axes of the first basic coil system (1, 22a, 32a, 42a), of the second basic coil system (2, 22b, 32b, 42b) and of the third basic coil system (3, 22c, 32c, 42c) are oriented orthogonally with respect to the surface of the workpiece during measurement, - with the result that an independent measured value for determining a complete internal stress tensor can be obtained by means of each basic coil system, from which the mechanical surface stresses of the workpiece can be at least partially determined.