  We report the first observation of the de Haas-van Alphen (dHvA) effect in
the novel spin-triplet superconductor UTe2 using high quality single crystals
with the high residual resistivity ratio (RRR) over 200. The dHvA frequencies,
named alpha and beta, are detected for the field directions between c and
a-axes. The frequency of branch beta increases rapidly with the field angle
tilted from c to a-axis, while branch alpha splits, owing to the maximal and
minimal cross-sectional areas from the same Fermi surface. Both dHvA branches,
alpha and beta reveal two kinds of cylindrical Fermi surfaces with a strong
corrugation at least for branch alpha. The angular dependence of the dHvA
frequencies is in very good agreement with that calculated by the generalized
gradient approximation (GGA) method taking into account the on-site Coulomb
repulsion of U = 2 eV, indicating the main Fermi surfaces are experimentally
detected. The detected cyclotron effective masses are large in the range from
32 to 57 m0 . They are approximately 10-20 times lager than the corresponding
band masses, consistent with the mass enhancement obtained from the Sommerfeld
coefficient and the calculated density of states at the Fermi level. The local
density approximation (LDA) calculations of ThTe2 assuming U4+ with the 5f^2
localized model are in less agreement with our experimental results, in spite
of the prediction for two cylindrical Fermi surfaces, suggesting a mixed
valence states of U4+ and U3+ in UTe2.
