We present high field magnetoresistance, Hall effect and thermopower measurements in the Isingtype ferromagnetic superconductor UCoGe. Magnetic field is applied along the easy magnetization c axis of the orthorhombic crystal. In the different experimental probes we observed five successive anomalies at H ≈ 4, 9, 12, 16, and 21 T. Magnetic quantum oscillations were detected both in resistivity and thermoelectric power. At most of the anomalies, significant changes of the oscillation frequencies and the effective masses have been observed indicating successive Fermi surface instabilities induced by the strong magnetic polarization under magnetic field.PACS numbers: 71.27.+a, 71.18.+y, 74.70.Tx Lifshitz transitions (LTs) are continuous quantum phase transitions at zero temperature where the topology of the Fermi surface (FS) changes due to the variation of the Fermi energy and the band structure of a metal [1,2]. They have been already studied in the sixties and can be induced by chemical doping, pressure, or strong magnetic field (H). However, only recently LTs have been proposed as the driving force to modify the ground-state properties in strongly correlated electron systems. The interplay of a LT with magnetic quantum phase transitions in heavy fermion systems has been treated in various theoretical models (see e.g. Refs. 3-8). The influence of LTs on the appearance of superconductivity is discussed in cuprates [9,10], iron pnictides [11,12] Usually the electronic band structure is a rather robust property of the metallic state, especially when applying magnetic fields. Only when the magnetic ground state is modified, changes of the FS may be detected. In a normal metal the Zeeman splitting induced by accessible magnetic fields is weak with respect to the Fermi energy which is usually of the order of a few eV. Importantly, in heavy fermion compounds the Fermi energy scale is significantly reduced due to the hybridization of the conduction and the localized f electrons. Thus, the Zeeman splitting of the flat bands crossing the Fermi level can be so strong that one of the spin-split FS sheets is continuously suppressed and undergoes a LT. In heavyfermion systems a LT is often associated to a change in the intersite and/or local magnetic fluctuations, see e.g. In this Letter we report on FS properties of UCoGe under magnetic field, which orders ferromagnetically at T C = 2.7 K. Remarkably, homogeneous coexistence of ferromagnetism and heavy-fermion superconductivity is observed below T sc = 0.6 K [23]. UCoGe crystallizes in an orthorhombic structure (space group P nma). In order to study the field dependence of the FS properties in a highly polarizable heavy fermion system with small FS pockets we performed systematic resistivity (ρ), Hall effect (ρ xy ) and thermopower (S) experiments in UCoGe. Two different samples (labelled S1 and S2) with residual resistivity ratios [RRR = ρ(300 K)/ρ(1 K)] of 105 and 36 have been prepared for experiments with electrical or heat current along the b and a axis respectively.