  We present different transport measurements up to fields of 29~T in the
recently discovered heavy-fermion superconductor UTe$_{2}$ with magnetic field
$H$ applied along the easy magnetization a-axis of the body-centered
orthorhombic structure. The thermoelectric power varies linearly with
temperature above the superconducting transition, $T_{SC}= 1.5$ K, indicating
that superconductivity develops in a Fermi liquid regime. As a function of
field the thermolelectric power shows successive anomalies which are attributed
to field-induced Fermi surface instabilities. These Fermi-surface instabilities
appear at critical values of the magnetic polarization. Remarkably, the lowest
magnetic field instability for $H\parallel a$ occurs for the same critical
value of the magnetization (0.4 $\mu_B$) than the first order metamagnetic
transition at 35~T for field applied along the $b$-axis. The estimated number
of charge carriers at low temperature reveals a metallic ground state distinct
from LDA calculations indicating that strong electronic correlations are a
major issue in this compound.
