UTe2 attracts much attention because of spin-triplet supercondudctivity and unusual properties. It crystallizes in the body-centered orthorhombic structure with the space group, Immm (#71). The large Sommerfeld coefficient (γ=120 mJ K-2mol-1) manifests a heavy electronic state. Superconductivity occurs at 1.5-2K in the paramagnetic ground state. One of the highlights in UTe2 is the huge upper critical field, Hc2, exceeding the Pauli limit. In particular, the field-reentrant superconductivity appears up to the first-order metamagnetic transition at Hm=35T. Thus the spin-triplet state is naively expected. Microscopic evidence for the spin-triplet state is indeed obtained from the Knight shift in NMR experiments. At the moment of the discovery of superconductivity, UTe2 had been thought to be at the verge of ferromagnetic order with strong ferromagnetic fluctuations from the similarity to the ferromagnetic superconductors, URhGe and UCoGe, where the field-reentrant (-reinforced) superconductivity is observed when the field is applied along the hard magnetization axis, leading to the development of ferromagnetic fluctuations. In UTe2, ferromagnetic fluctuations are, however, not confirmed experimentally, alternatively, antiferromagnetic fluctuations with the incommensurate q-vector are detected in the inelastic neutron scattering experiments. In UTe2, multiple fluctuations antiferromagnetic/ferromagnetic fluctuations as well as valence, and Fermi surface instabilities may play important roles for superconductivity. Another important highlight in UTe2 is the multiple superconducting phases under pressure and the field-induced phenomena, which also support a spin-triplet scenario because of the spin and orbital degree of freedom. In this talk, we present our recent progress on UTe2, focusing on the high quality single crystal growth and superconducting properties.
 See review paper,for example, D. Aoki, J. P. Brison, J. Flouquet, K. Ishida, G. Knebel, Y. Tokunaga, Y. Yanase, J. Phys.: Condens, Matter. 34, 243002 (2022).