A multi-core optical fiber (100; 100A-100E) comprising a plurality of core parts each extending along a predetermined axis, a cladding integrally covering each of the plurality of core parts, and a coating provided on an outer peripheral surface of the cladding, characterized in that: as to an effective area of a fundamental mode in at least any one of the plurality of core parts, the effective area at a first wavelength in the range of 1 μm to 2.5 μm is not more than 87 μm 2, each of the plurality of core parts is comprised of silica glass, and non-linear refractive indices n 2 of the respective core parts at a second wavelength in the range of 1.26 μm to 1.65 μm are in the range of 2 × 10 -20 to 3 × 10 -20 [m 2 /W], and the multi-core optical fiber satisfies at least one of first to third conditions at the first wavelength, the first condition being defined in that: each of the core parts enables single-mode transmission at the first wavelength, and Expression below is satisfied: N core A coat log 2 1 + exp − 80 η n 2.10 × 10 10 10 8 α dB, n − 1 3 α dB, n 10 8 α dB, n D n n 2, n A eff, n 2 log 5.47 × 10 3 D n 1 − 10 − 8 α dB, n α dB, n 1 3 + 1 − exp − 80 η n ≥ 7 × 1.96 × 10 2 where α dB,n [dB/km] represents a transmission loss at the first wavelength of a core part n with the largest crosstalk from other core parts out of the plurality of core parts, n 2,n [m 2 /W] a non-linear refractive index of the core part n at the first wavelength, A eff,n [μm 2] an effective area of the core part n at the first wavelength, D n [ps/(nm·km)] a chromatic dispersion of the core part n at the first wavelength, η n [/km] a sum of power coupling coefficients to the core part n from all the other core parts at the first wavelength, N core the number of core parts in the multi-core optical fiber, and A coat [mm 2] a cross sectional area of the entire multi-core optical fiber on a cross section orthogonal to the predetermined axis, the second condition being defined in that: each of the core parts enables single-mode transmission at the first wavelength, and Expression below is satisfied: 1 A coat ∑ n log 2 1 + exp − 80 η n 2.10 × 10 10 10 8 α dB, n − 1 3 α dB, n 10 8 α dB, n D n n 2, n A eff, n 2 log 5.47 × 10 3 D n 1 − 10 − 8 α dB, n α dB, n 1 3 + 1 − exp − 80 η n ≥ 7 × 1.96 × 10 2 and and the third condition being defined in that: a transmission loss of a spatial mode not guided with the transmission loss of not more than 1 dB/km at the first wavelength, is not less than 0.9 dB/m, and Expression below is satisfied: 1 A coat ∑ n ∑ m log 2 1 + exp − 80 η n 2.10 × 10 10 10 8 α dB, nm − 1 3 α dB, nm 10 8 α dB, nm D nm n 2, nm A eff, nm 2 log 5.47 × 10 3 D nm 1 − 10 − 8 α dB, nm α dB, nm 1 3 + 1 − exp − 80 η n ≥ 7 × 1.96 × 10 2 where α dB,nm [dB/km] represents a transmission loss at the first wavelength of an mth spatial mode guided with the transmission loss of not more than 1 dB/km at the first wavelength out of spatial modes in an nth core part among the plurality of core parts, n 2,nm [m 2 /W] a non-linear refractive index at the first wavelength of the mth spatial mode in the nth core part, A eff,nm [μm 2] an effective area at the first wavelength of the mth spatial mode in the nth core part, and D nm [ps/(nm·km)] a chromatic dispersion at the first wavelength of the mth spatial mode in the nth core part. as to an effective area of a fundamental mode in at least any one of the plurality of core parts, the effective area at a first wavelength in the range of 1 μm to 2.5 μm is not more than 87 μm 2, each of the plurality of core parts is comprised of silica glass, and non-linear refractive indices n 2 of the respective core parts at a second wavelength in the range of 1.26 μm to 1.65 μm are in the range of 2 × 10 -20 to 3 × 10 -20 [m 2 /W], and the multi-core optical fiber satisfies at least one of first to third conditions at the first wavelength, the first condition being defined in that: each of the core parts enables single-mode transmission at the first wavelength, and Expression below is satisfied: each of the core parts enables single-mode transmission at the first wavelength, and Expression below is satisfied: where α dB,n [dB/km] represents a transmission loss at the first wavelength of a core part n with the largest crosstalk from other core parts out of the plurality of core parts, n 2,n [m 2 /W] a non-linear refractive index of the core part n at the first wavelength, A eff,n [μm 2] an effective area of the core part n at the first wavelength, D n [ps/(nm·km)] a chromatic dispersion of the core part n at the first wavelength, η n [/km] a sum of power coupling coefficients to the core part n from all the other core parts at the first wavelength, N core the number of core parts in the multi-core optical fiber, and A coat [mm 2] a cross sectional area of the entire multi-core optical fiber on a cross section orthogonal to the predetermined axis, the second condition being defined in that: each of the core parts enables single-mode transmission at the first wavelength, and Expression below is satisfied: the third condition being defined in that: a transmission loss of a spatial mode not guided with the transmission loss of not more than 1 dB/km at the first wavelength, is not less than 0.9 dB/m, and Expression below is satisfied: